Body is an informal game term. A character's body consists of its strength and vitality, as well as occasionally other attributes like its race, signet, or unloaded keywords that other cards might spot. Broadly, the "body" is the function a character serves other than its game text. This term comes from Magic: the Gathering.
For example, many Elven decks play Glorfindel, Revealed in Wrath (9R+16) for his high strength, respectable vitality, and low Twilight cost in a starting Fellowship; his game text is a secondary consideration. Likewise, Moria decks sometimes use Troll’s Keyward (1R199) for his respectable strength and relatively high vitality, even if they aren't running Cave Troll of Moria, Scourge of the Black Pit (1R165) at all.
Oftentimes, a character card played chiefly for its gametext is referred to as "(gametext) with a body" or "on a stick". For example, Ranger of Westernesse (11S65) is Pathfinder (1C110) on a stick. This usage also comes from the Magic: the Gathering community.
Body is also occasionally used as a verb, to mean defeating another player easily. This usage comes from the fighting game community, although it has spread to many other types of competitive online games.