In
Ludwig Wittgenstein's work a 'language game' is an
imaginary restricted language or a strand of actual linguistic practice.
A chess analogy: pieces (words) are moved (spoken) according to rules (grammar, custom). Moves (utterances) have significance (meaning) in the context of a game (language). Understanding meaning is competence to 'make a move' in language.
So much for Bertrand Russell's, Gottlob Frege's and the Tractatus's attempts to ground meaning outside language ...