A gridded sheet, typically gridded in 1" (~25mm) squares, used for showing tactical situations on the table. Often used with miniatures, tho sometimes cardboard tokens are used.
Half-inch square grids were not uncommon for use with 15mm miniatures and 1/2" cardboard counters, and were generally used for Traveller, FASA's Star Trek, and TSR's Gang Busters and Star Frontiers games.
1" squares are the most common, and are used with D&D, Warhammer FRP (1st and 2nd eds), and several other well known FRPs, due to the wide range of 25/28/30/32mm miniature figures, and 1" round "tokens" of either wood or cardboard.
1" (~25mm), 30mm, and 35mm hexagonal grids are also fairly common; Warhammer FRP included specific adaptations, and GURPS, Hero System, The Fantasy Trip, Dragonquest, and several other older games specifically called for hex grids.
16mm hex grids are the standard for counter-on-map wargames, such as Star Fleet Battles, Starfire, Ogre/GEV, and some gamers used them with 1/2" square counters for RPG use as well.
Almost a synonym of Battlemat. Many games use the terms interchangably.
Many D&D battlemaps are actually printed scenes overlaid with a square grid.