Tail-Twig Clippers: Part of a broom maintenance kit.
Tales of Beedle the Bard, The (DH ch. 7): A book of old children's stories. Of course we all know there's no reason to be reading children's books...
Tarantallegra: An incantation that makes the target dance uncontrollably.
Etym: From Italian tarantella, a type of dance, and allegra "fast" (also a musical term).
Ted [Theodore] (PS ch. 1): Name of a newsreader the Dursleys watch.
Etym: Greek, "god's gift".
Etym: See above.
Etym: See above.
Tenebrus (OotP ch. 21): Hagrid's favorite of the thestrals, the first one born in the Forbidden Forest.
Etym: Altered spelling of tenebrous.
Terence Higgs: Etym: From Latin Terentius, the name of a Roman gens of unknown etymology.
Tergeo (HBP ch. 8): An incantation used to wipe away blood.
Etym: Latin, "I wipe, correct".
Etym: See above.
thestrals (OotP ch. 10): Big skeletal carrion-eating black winged horses visible only to those who have seen death. Understandably, they have a bit of a bad reputation.
Etym: From an archaic word, thester "darkness".
Thicknesse, Pius (DH ch. 1): Scrimgeour's successor as Minister of Magic.
Etym: In the UK, a person who is stupid is said to be thick.
Thief's Downfall (DH ch. 26): A sort of anti-magic waterfall utilized by Gringotts.
Thomas, Dean (PS ch. 7): A Gryffindor, the same year as Harry, and a member of Dumbledore's Army. From a Muggle family, he is a big fan of the West Ham soccer team.
Etym: From Aramaic meaning "twin". We can also consider Thomas the Rhymer, a 13th century Scottish poet and prophet who in popular lore is connected with Merlin.
Thorfinn Rowle: Etym: An old Norse name. Thorfinn Karlsefni led one of the colonizing expeditions to North America.
Three Broomsticks: The pub in Hogsmeade.
Tibbles, Mr. (PS ch. 2): One of Mrs. Figg's cats.
Tiberius Ogden: Etym: The name of 2 Roman emperors, etymology unknown.
Tiberius (HBP ch. 7): Cormac McLaggen's uncle, who may or may not be the same as the above.
Etym: See above.
Time Room: The room in the Department of Mysteries for time-related research.
Timms, Agatha (GoF ch. 7): Etym: Etymology unknown; possibly cognate to the Germanic name Timmo, of unknown meaning.
Tinworth (DH ch. 16): Supposedly a village in Cornwall, but I can't find any record of it.
Tobias Snape: Etym: From a Hebrew name meaning "Jehovah is good", the main character of the book of Tobit.
Tofty, Professor (OotP ch. 31): Griselda Marchbanks's assistant in performing O.W.L. exams.
Etym: From Middle English toft "homestead".
Toujours Pur (OotP ch. 6): The motto of the Black family.
Etym: French, "always pure".
Tom (PoA ch. 3): The proprietor of The Leaky Cauldron.
Etym: From an Aramaic word meaning "twin". One of the twelve apostles, whose real name may have been Judah; the nickname would have been used to distinguish him from Judah the brother of James (St. Jude), and Judah of Kerioth (Judas Iscariot).
Tongue-Tying Curse: A spell to prevent vocalization. Incantation: Langlock.
Tonks, Andromeda Black (OotP ch. 3): Sirius's cousin; Nymphadora's mother.
Etym: Patronymic from a diminutive form of Thomas.
Tonks Lupin, Nymphadora: Etym: See above.
Tonks, Ted (OotP ch. 3): Nymphadora's father, a Muggle.
Etym: See above.
Ton-Tongue Toffee: A joke candy created by Fred and George Weasley which enlarges the eater's tongue beyond all belief.
Toothflossing Stringmints: A type of candy available at Honeydukes.
Tottenham Court Road (DH ch. 9): A major street in London.
Towler, Kenneth (OotP ch. 12): A student, probably a Gryffindor, two years ahead of Harry.
Etym: Name for a toll taker or tax gatherer, from Middle English toll "tax, payment".
trading cards: See Famous Witches and Wizards.
Transfiguration: One of the basic subjects at Hogwarts, it concerns the changing of things from one form to another. The Transfiguration teacher is Professor McGonagall.
Transfiguration Today: A wizard publication.
Transmogrifian Torture: A deadly spell that Lockhart claimed to know about.
Travels with Trolls: One of Gilderoy Lockhart's books.
Travers: A Death Eater, imprisoned in Azkaban until recently.
Etym: Name for someone who lived by a bridge or ford, or a gatherer of tolls, from Middle English/Old French travers "passage, crossing". Or, an Anglicized form of Gaelic Ó Treabhair, from a byname meaning "industrious, prudent".
treacle tart: A syrupy pastry usually served with custard.
Trelawney, Cassandra (OotP ch. 15): Professor Trelawney's great-great-grandmother, a seer of some reknown.
Etym: See below.
Trelawney, Sibyll Patricia: The Divination instructor and constant predictor of woe.
Etym: Placename, from Cornish tre "homestead, settlement" + an element of unknown meaning.
Trevor (PS ch. 6): Neville Longbottom's toad.
Etym: From Welsh tre(f) "homestead, settlement" + mawr "large", or Gaelic Ó Treabhair, from a byname meaning "industrious, prudent".
Trip Jinx (OotP ch. 27): A spell to trip someone.
trifle: A confection made of layers of sherry-soaked sponge cake, jelly, and custard, usually topped with whipped cream and fruit.
Trimble, Quentin (PS ch. 5): Author of The Dark Forces: A Guide to Self-Protection.
Etym: From an Old English personal name, formed from trum "strong, firm" + beald "bold, brave". On the other hand, also an obsolete form of tremble.
Triwizard Cup: The trophy of the Triwizard Tournament.
Triwizard Tournament: A competition between champions selected from Beauxbatons, Durmstrang, and Hogwarts chosen by the Goblet of Fire. Originally established 700 years ago and meant to be held every five years, but discontinued in recent centuries owing to a high fatality rate. It was resurrected in Harry's fourth year.
trolls: Large, stupid humanoid creatures that like to fight with clubs.
Troy (GoF ch. 8): A Chaser on the Irish national Quidditch team.
Etym: An Anglicized form of Ó Troighthigh, from a byname meaning "foot soldier".
True Seer: One with the gift of prophecy.
tubeworms: This term covers a whole range of polychaete worms.
Tufty (PS ch. 2): One of Mrs. Figg's cats.
Turpin, Lisa (PS ch. 7): A Ravenclaw, same year as Harry.
Etym: A number of possibilities here, but my favorite is Dick Turpin (1706-1739), an English highwayman, the subject of Rookwood.
Tutshill Tornadoes (OotP ch. 10): Cho Chang's favorite Quidditch team, presently leading their league. Tutshill is not a real place.
Twelve Fail-Safe Ways to Charm Witches (DH ch. 7): An advice book for wizards on how to improve their dating skills and, um, wandwork.
Twilfitt and Tatting (HBP ch. 6): A clothier in Diagon Alley.
Etym: The first is a contraction of it will fit; tatting is lacemaking.
Twitchy Ears: A curse that makes the target's ears wiggle.
Twycross, Wilkie (HBP ch. 18): An Apparation instructor dispatched to Hogwarts.
Etym: No etymology for the name, but it's a town with a famous zoo.