Definition of committed
Literally "engaged". A situation where a player is said "committed" at poker is a situation where he no longer has a choice to be all in considering what he has already invested in the pot, the size of the pot and its equity in the hand. "I'm committed, I have no choice anymore, I have to call". When you're committed to a pot, it doesn't mean you think you'll win the hand often, but we know that in the long run, it's still the game to play.
An example of a committed hand
You are in tournament with A2 on the button. You open your hand preflop after the players before you have folded. The two blinds call your raise. The flop gives 4-5-8 with two spades. The small blind bets the flop, the big blind calls, you raise to 12 big blinds (all the players had 50 big blinds before the hand started), the small blind pushes to all-in, the big blind calls and the floor is yours. Here you have only one draw on the ace. It is possible that one or both players may have a much stronger hand than you, but given all the money in the pot and your equity, you are committed to pot and you have to call all in.