The story
X signifies an arbitrary lexical category; certain structures are represented by this letter and an overbar.
Etymology from Wiktionary, CC BY-SA 4.0.
X-bar theory
Today it means: A theory that posits a common syntactic structure for different lexical categories. Each phrase (XP) is the projection of a head (X) and may optionally include a specifier (sister of X-bar, daughter of XP), adjuncts (sister and daughter of X-bar) and complements (sister of X, daughter of X-bar). Full definition →