A player has the initiative or momentum when they are able to decide where to play next, and in particular, when they are not forced to answer their opponent's last move. A player with the initiative is often able to play forcing moves that the opponent must answer, and can thereby keep the initiative, possibly for many moves. When the player makes a move that is insufficiently forcing, they may lose the initiative, and the other player may gain the initiative.
Since the player who has the initiative is dictating play, having the initiative is a great advantage, and often turns out to be decisive. A player should generally not hand over the initiative to the opponent, unless there is a very good reason for doing so. In well-played close matches, the initiative often swings between the two players with each move.
Having initiative is sometimes called sente, and its opposite, i.e., not having initiative, is sometimes called gote. These Japanese terms are adopted from the game of Go.
In the endgame, it sometimes happens that the two players play a sequence of moves that are mutually forcing, so that if one player deviates from the sequence of moves, the other player immediately wins. In that case, neither player has the initiative, and the game just continues along a predetermined route until one player gains the initiative again.
Initiative can sometimes be local, i.e., we can say that a player has the initiative in a certain area of the board. The opponent may be able to delay responding to the player's move in that area by first playing a forcing move elsewhere, but will eventually have to come back to responding in the area in question.
In a ladder, the attacker usually has the initiative, because the attacker can decide whether and when to pivot, whether to play a cornering move, etc. On the other hand, the defender usually has little choice but to push the ladder, or perhaps to yield.