Hagrid, Rubeus: The Keeper of the Keys and Grounds at Hogwarts, a giant of a man with a heart to match, especially when it comes to exotic and dangerous animals (cf. Norbert and Fluffy). Wand (supposedly destroyed, but strongly hinted to be hidden in his umbrella): oak, bendy, 16".
Etym: According to Rowling, "If you were hagrid-- it's a dialect word-- you'd had a bad night. Hagrid is a big drinker-- he's had a lot of bad nights."
In-depth article at HPLexicon
Hair-Raising Potion: Something that includes rat tails as an ingredient.
Hair-Thickening Charm (OotP ch. 19): Something that could conceivably cause someone's eyebrows to get huge.
Handbook of Do-It-Yourself Broomcare: A book Hermione gave to Harry.
Handbook of Hippogriff Psychology: A book Ron consulted to defend Buckbeak.
Hand of Glory: An item associated with dark magic since medieval times. Usually said to be the hand of a thief or murderer hanged at midnight, modified to allow candles to be socketed in its fingertips. In this series, it provides light only to the holder.
Hanged Man, The: The pub in Little Hangleton.
Hannah Abbott: Etym: From Hebrew for "He (God) has favored me". In the Bible, the mother of Samuel, and in the Talmud, a prophetess; her prayer exemplifies successful petitions to God.
Harkiss, Ciceron (HBP ch. 4): Ambrosius Flume's first employer.
Etym: From Hard, meaning "hardy, brave, strong", or a stern man.
Harold Dingle: Etym: Derives from the Old English words here "host, army" + weald "power".
Harper (HBP ch. 14): A student a year behind Harry; Draco Malfoy's stand-in as Slytherin Seeker for one game.
Etym: Occupation name, also seen as an error for harpy.
Harry James Potter: Etym: Stated by Rowling on numerous occasions to just be her favorite male name.
Hassan Mostafa: Etym: Means "beautifier".
Hawkshead Attacking Formation: A Quidditch move which involves the three Chasers flying close together.
Head Boy: A seventh-year student chosen for leadership and scholastic abilities who shares the prefects' duties.
Head Girl: A seventh-year student chosen for leadership and scholastic abilities who shares the prefects' duties.
Head Hockey: A pastime of the Headless Hunt.
Headless Hat (OotP ch. 24): Another fine product of Weasley's Wizard Wheezes which causes the wearer to appear decapitated.
Headless Hunt: A mass of headless ghosts who won't let Nearly Headless Nick join them.
Head Polo: Another pastime of the Headless Hunt.
Healer (OotP ch. 22): One of the medical staff at St. Mungo's Hospital. Their symbol is a crossed wand and bone.
Healer's Helpmate, The (HBP ch. 5): A book Molly Weasley used for first aid advice.
Hebridean Black: A type of dragon native to the British Isles.
Hector Dagworth-Granger: Etym: One of the major figures in the Trojan War. The name is from Greek ekhein "check, restrain", and can also mean a swashbuckler, braggart, or bully.
Hedwig: Harry's owl, named after someone he read about in A History of Magic. Cut down in her middle age by an errant Killing Curse aimed at Harry.
Etym: Stated by Rowling to be a medieval saint, which would be St. Hedwig of Andechs. Another possibility is the devout but not canonized medieval woman who was crowned "king" of Poland at the age of 9, strongly supported religion and scholarship, and caused the restoration of the university of Kraków, which became the Jagiellonian University. (Here's the English root page.)
Helena Ravenclaw: Etym: Variant of the Greek name Helen, "the bright one". The name of the sainted mother of Constantine the Great.
Helga Hufflepuff: Etym: From Norse, meaning "holy". Also an alternate name for St. Olga (890-969), the first recorded female ruler in Russa, the first Russian royal to adopt Christianity, and the first Russian Orthodox saint.
heliopath (OotP ch. 16): Fire spirits that Cornelius Fudge allegedly has a private army of.
Etym: Greek helio- "sun" + -path in the sense of "sympathetic to, sharing the quality of".
hellebore (OotP ch. 12): Can refer to various plants in the genera Helleborus and Veratrum, believed to have medicinal properties. Syrup of hellbore is an ingredient in the Draught of Peace.
Hengist of Woodcroft (PS ch. 6): Was featured on a Famous Witches and Wizards trading card. Might be an actual historical person, but I haven't found any info on him.
Heptomology (OotP ch. 25): Some kind of divination.
Etym: Hept- indicates it involves the number 7 in some way.
Hepzibah Smith: Etym: Also spelled Hephzibah, a Biblical name meaning "my delight is in her". The name of mother of Manasseh, and also used as a figurative name for Israel.
Herbert Chorley: Etym: From Old German harja "host, army" + berhta "bright".
Hereward (DH ch. 21): The son of Godelot, who killed him for the Elder Wand.
Etym: Hereward the Wake was a semi-historical Saxon outlaw.
Hestia Jones: Etym: The Greek goddess of the hearth.
Hetty Bayliss [Henrietta]:
Etym: Feminine of Henry from Old German haimi "house, home" + ric "ruler".
Herbology: A required course at Hogwarts, taught by Professor Sprout.
Hermes (CoS ch. 3): Percy's owl, a screech owl, bought for him when he became a prefect.
Etym: The Greek name for the messenger of the gods, also the god of thieves, children, and travellers.
Hermione Granger: Etym: A derivative of Hermes. Used by Shakespeare in A Winter's Tale as the name of a queen falsely accused of adultery, who dies of the shock when the evidence in her favor is disregarded.
Hiccuping Solution (HBP ch. 22): A potion Draco Malfoy made but not very well.
Hiccup Sweet: Something available at Zonko's Joke Shop.
Higgs, Bertie (HBP ch. 7): One of Cormac McLaggen's uncle's companions on nogtail hunts.
Etym: See below.
Higgs, Terence (PS ch. 12): The Seeker for the Slytherin Quidditch team in Harry's first year, replaced by Draco Malfoy later on.
Etym: From the medieval given name Hicke, a form of Richard, whose etymology is uncertain; may be riic "ruler" + heard "hard".
High Inquisitor (OotP ch. 15): A post created for Dolores Umbridge giving her authority of inspection and dismissal over the other teachers. The real-world equivalent is Ofsted.
hinkypunk: A one-legged creature which lures travelers to their death in bogs.
Etym: Usually spelled Hinky-Punk, this is a local equivalent to the will-o'-the-wisp on the Somerset-Devon border.
Hippocrates Smethwyck: Etym: After the most important medical figure of ancient times.
hippogriff: A mythical creature with the head, wings, and legs of an eagle and the hindquarters of a horse. In these books, a proud and demanding creature that requires a person to show respect before they can approach it.
History of Magic: A required course at Hogwarts, taught by Professor Binns.
Hit Wizards: The toughest portion of the Department of Magical Law Enforcement.
Hobgoblins, The (OotP ch. 10): A band that Sirius Black is alleged to have led under the name Stubby Boardman.
Hog's Head, The (OotP ch. 16): The wrong-side-of-the-tracks bar in Hogsmeade.
Hogsmeade: The only entirely non-Muggle settlement in the British Isles, located near Hogwarts. Local businesses and features include the Three Broomsticks, the Hog's Head, Madam Puddifoot's tea shop, the Shrieking Shack, Honeydukes, a branch of Gladrags Wizardwear, Scrivenshaft's Quill Shop, Dervish and Banges, and Zonko's Joke Shop.
Etym: -meade in English placenames refers to a piece of grassland; thus, it's the meadow near Hogwarts. Interesting that the school appears to have preceded the village (unless both were named after some other local feature).
Hogwarts: The school for young wizards in the British Isles, housed in a massive castle with 142 shifting staircases, living paintings, numerous ghosts, and pretty much everything else that would have made your school the least bit interesting.
Hogwarts Express: The train that runs from King's Cross to Hogwarts at the beginning of the school year, and back at the end.
Hogwarts, a History: One of the books Hermione read to get ready for the start of school.
Holidays with Hags: One of Gilderoy Lockhart's books.
Hokey (HBP ch. 20): The aged house-elf of Hepzibah Smith.
Etym: A word meaning old and overused; also a petty oath.
holly: Shrubs and trees of the genus Ilex, reputed to have protective powers. Harry's wand probably was made with English holly (I. aquifolium).
Etym: Rowling has given her reason for using it as its association with life and also with the word holy. Unfortunately, the second part is folk etymology; the word holly goes back to an Indo-European stem meaning "to prick". (Hollyhock, on the other hand, evolved from holy hock.)
Holyhead Harpies (HBP ch. 4): A professional Quidditch team. Holyhead is a ferry port in Wales.
Home Life and Social Habits of British Muggles: The textbook for the Muggle Studies class.
Homenum revelio (DH ch. 9): An incantation which is supposed to reveal hidden people... well, humans, anyway.
Etym: Sort of Latin for "I reveal a person". (Should start Hominum...)
Homorphus Charm: The spell with which Lockhart claims to have cured the Wagga Wagga Werewolf. He probably made it up-- it appears the Wolfsbane Potion is the only effective countermeasure.
Honeydukes: The candy store in Hogsmeade.
Etym: No info; also invented?
honking daffodils (OotP ch. 27): A variety cultivated by Professor Sprout.
Hooch, Madam: The flying instructor at Hogwarts, and usually the referee for inter-house Quidditch games.
Etym: No etymology. There was a minor Dutch painter named Pieter de Hooch, or Hoogh, or Hooghe (1629-1684).
Hooper, Geoffrey (OotP ch. 13): A Gryffindor who tried out to be the Keeper on their Quidditch team.
Etym: Occupational name for a craftsman who would fit hoops on casks, barrels, etc., from Middle English hoop "hoop, band".
Hopkirk, Mafalda (CoS ch. 2): Someone in the Improper Use of Magic Office.
Etym: From Hopekirk, named from Northern Middle English hop(e) "valley among hills" + kirk "church". A former Hufflepuff?
Horace E. F. Slughorn:
Etym: Couldn't find an etymology, but this is the name under which the poet Quintus Horatius Flaccus is best known.
Horcrux (HBP ch. 17): A container used to hide a piece of a wizard's soul.
Etym: The first element may be Latin horreum "barn, storehouse"; don't know about the second.
hornbeam: Various hardy, slow-growing trees of the birch family grown for timber and ornament. The wood is valued for toughness.
Hornby, Olive (CoS ch. 16): A girl who particularly tormented Moaning Myrtle and was haunted by Myrtle for it until the day she (Olive) died what seems like an awfully early death.
Etym: Name of several places in northern England, from the Old Norse name Horni "horn" + býr "farm, settlement".
Horseback Head-Juggling: Another pastime of the Headless Hunt.
house-elf: A magical creature, bound to a specific wizard family or place, which does housekeeping tasks. If a house-elf's employer hands a piece of clothing to them, the elf is considered dismissed.
House-elves are based on brownies, mostly benevolent spirits said to inhabit particular houses or farmsteads and do chores when no one is looking. One can leave bread or a bowl of milk or cream out for the brownie to show thanks, but making any more extravagant gifts will offend it, which will turn to mischief. If a suit of clothes is made for a brownie, it will put them on and disappear.
House-Elf Liberation Front: Hermione's current effort to better the conditions of house-elves.
Hover Charm: A spell used to make something float in the air. Apparently detectable from a distance (unless someone from the Improper Use of Magic Office just happened to be nearby).
Howler: An angry voice recording which plays at full volume when opened, sent by parents to give public rebukes to their children at school; a nastygram.
Hufflepuff, Helga: One of the four founders of Hogwarts.
Etym: See below.
Hufflepuff House: One of the four houses of Hogwarts, it emphasizes hard work, goodness, and self-sacrifice. The house of the saints-- and martyrs. Badge: Or, a brock rampant reguardant, at best guess, anyway. House colors are supposed to be black and gold. The house ghost is the Fat Friar, and the head of the house is Professor Sprout.
See "In Defense of Hufflepuff" for more on the house philosophy.
Etym: Invented; along the lines of "huff and puff".
Hugo Weasley: Etym: Name derived from Germanic hug, "heart, mind, spirit", which suggests an eventual Hufflepuff. Also the name of Rowling's first non-children's book award, regardless of what the W. H. Smith people say.
Humberto: see The Great Humberto.
Humphrey Belcher: Etym: From Old English hun "bear-cub, warrior" + frith "peace". Also, "to dine with Duke Humphrey" is to not eat.
Hungarian Horntail: A particularly large and nasty species of dragon.
Hurling Hex: A malignant spell which can be cast on a broomstick.