Improper Use of Magic Office: The arm of the Ministry of Magic which, among other things, keeps tabs on any students who try to use magic outside of school.
incantations: The verbal components of spells. Incantations come in a variety of languages. Oddly, modern-language spells which contain verbs are in the imperative (the command form) but the Latin ones are in the indicative (that is, descriptive of action). There may be a deep reason for this, but it's probably just because Rowling was never forced to take Latin. I was, and by golly I'm going to get some use out of it. Imperative forms are provided for the curious.
Inter-House Championship: The competition between the Hogwarts houses to see which can accumulate the most points by the end of the year.
International Confederation of Warlocks: Some sort of multinational professional association.
Invisibility Booster: Something that can make a flying car invisible, at least to Muggles.
invisibility cloak: An extremely rare magical item which makes the wearer(s) totally invisible to normal sight, though it is penetrable with any kind of magical sight. Harry's father left one to him.