When a player is tackled, the play is stopped when his knee touches the ground. Quarterbacks can use this rule in the final play of the half/game - instead of making a play which might result in a turnover, they can simply kneel down to end the play.
It annoys me that I'm not sure exactly where taking a/the knee comes from originally. I think it's something to do with one, of all of:
possibly based on:
possibly based on religious supplicatory position?