In two-or-more-player sequential games, a ply is one turn taken by one of the players.
Thus, after 20 moves in a chess game, 40 plies have been completed—20 by white and 20 by black.
For instance, in heads up Texas hold'em, a street consists of 2 plies, with possible plays being check/raise/call/fold: the first by the player at the big blind, and the second by the dealer, who posts the small blind; and there are 4 streets: preflop, flop, turn, river (the latter 3 corresponding to community cards).
[2] Arthur Samuel first used the term in its game-theoretic sense in his seminal paper on machine learning in checkers in 1959,[3] but with a slightly different meaning: the "ply", in Samuel's terminology, is actually the depth of analysis ("Certain expressions were introduced which we will find useful.
The Deep Blue chess computer which defeated Kasparov in 1997 would typically search to a depth of between six and sixteen plies to a maximum of forty plies in some situations.