Caput Draconis: The first password to the Gryffindor tower when Harry arrives at Hogwarts.
Etym: Latin for "dragon's head".
Cauldron Cakes: A type of wizard candy, probably something akin to a cupcake.
centaur: A mythical creature with the body of a horse, and the top half of a human attached where the neck would be. Rowling's centaurs are largely peaceful but wish to keep to themselves. A group of them lives in the Forbidden Forest.
Etym: From ceorl, Old English for "a man".
Charms: One of the basic subjects that all students at Hogwarts have to study, taught by Professor Flitwick. A general term for all sorts of minor spells of instantaneous effect.
Chaser: One of the three players on a Quidditch team who pass the Quaffle between them and attempt to throw it through one of the goal hoops. A goal is worth 10 points.
Chocolate Frogs: A wizard candy, undistinguished except for the line of Famous Witches and Wizards trading cards that come with them.
Christmas pudding: A rich fruit pudding, typically splashed with brandy and set alight just before serving. Hiding a silver coin in it is also traditional.
Circe: An enchantress who figures in the Odyssey. She transformed Odysseus's crew into pigs. Featured on a Famous Witches and Wizards trading card.
Cliodna: A druid featured on a Famous Witches and Wizards trading card.
Cokeworth: Location of the Railview Hotel.
Comet Two Sixty: A brand of flying broom.
Common Welsh Green: A type of dragon native to the British Isles.
conk: British slang for "nose".
Cornelius Fudge: Etym: St. Cornelius was pope from 251 to 253, and is noted for taking a liberal attitude toward Christians who had renounced their faith under duress. He was succeeded by St. Lucius.
Crabbe: One of Draco Malfoy's cronies.
Etym: From a nickname for someone with an odd gait, like a crab, or a cantankerous person, as a shortening of crabapple.
Crockford, Doris (PS ch. 5): A particularly effusive fan of Harry's that he met in The Leaky Cauldron.
Etym: From the placename Crockford Bridge; further etymology is uncertain and probably not relevant. Also the name of a London gambling club, and the colloquial designation of a reference work produced by the Anglican Church.
curses: Spells that injure or impede the target. Some require only a wand and a quick incantation, but stronger ones require the caster to maintain line-of-sight and keep up the incantation for the full time of effect. The terms jinx and hex appear to be equivalent, and are used in curse names for alliterative effect. : A book seen in Diagon Alley.
Curse of the Bogies: Something Professor Quirrell mentioned in class. Bogie has varied meanings.