An annex is an extension of, or an addition to a building. A small room off of a main room is an annex, and attics are another type of annex.
As a noun, an annex is part of a building or an addition to a main structure, or it can be an attachment, as in "an annex to the current plans." When used as a verb, the word means something a little different. Sometimes annex is used as a nice word for "take" or "grab," as when Nazi Germany took the Sudetenland from Czechoslovakia in 1938 and added it to their own territory. In order to annex something to what is yours, you have to take it away from someone else.