A deck refers to one of several levels of a starship or similar vessel.
Aboard Earth starships, decks were usually named alphabetically; A-deck would be on top, B-deck right below it, etc. This naming scheme was used as early as 2069, in the SS Conestoga. (ENT: "Terra Nova", "The Catwalk")
By the 23rd century, Federation starships seem to have adopted another system, as the upper level was referred to as deck 1. Deck numbers then increased for each deck below, the lowest level having the highest number. For example, the Intrepid-class USS Voyager's lowest deck was deck 15. (VOY: "Good Shepherd")
However, aboard the refit Constitution-class USS Enterprise, the decks were ordered alphabetically again rather than numerically. The bridge was located on Deck A (as indicated by signage on the turbolift doors). Following an attack by Khan Noonien Singh in 2285, the turbolifts aboard the Enterprise were rendered inoperative below "C" Deck. (Star Trek II: The Wrath of Khan)