Push in poker is most commonly used when referring to an outcome in which two or more players are tied and split the pot. Additionally, it can also mean the action of going all-in, which can be called a shove in that case.
Push Poker Example:
You have a Qs Tc card, and two of your opponents have Qc Jc and Qd 9d hands, respectively. After the river card is revealed, the community board reads Ad Kh Jd Ts 5h. As all of you have a straight, the result is a push. Provided that you all put equal amounts in, each of you will receive exactly a third of the pot.