An act or statement is considered binding if it is not allowed to be undone or withdrawn.
In poker, this word is most often used to describe betting actions which are taken either verbally or physically (through hand signals or through motion of chips). Usually, this phrase is used to describe such actions when they have been made out of turn, but actions that are taken in turn are also binding.
The most common usage of the word binding is when a player verbally makes a betting action out of turn. If that action is a weak one, e.g. checking or folding, it is usually considered binding by a casino, and the player is required to take that action when it does become their proper turn. If the action is a strong one, e.g. betting or raising, often times the casino will allow the player to not take that action when it comes around to their proper turn -- but in other cases, a casino may require that the action be binding.
It is always best to play in turn, to avoid these types of situations.