Definition of push
A "push" is literally a "shove". A push is when a player takes his entire stack of chips and pushes them into the middle of the table. Therefore, he is all in. Pushes are usually associated with tournament poker. In tournament play, when a player is low on chips, he is in a "push or fold" position, meaning that his only viable options are to push all in or fold. In other words, there is no more room for maneuver as there was when he had a good stack. Normally, we can raise 3BB, bet the flop and fold if our hand is too weak and we have resistance, but when we have 6 big blinds for example, our options are limited.
Push or fold according to the Nash chart
In tournaments, when we have 15 big blinds or less, it's time to eliminate some options. Normally, you can fold, raise or 3bet or 4bet, etc., but with so few big blinds, there are only two options to consider: push or fold. To do this, you can use a chart based on Nash's equilibrium, the great mathematician. This chart will give you the range of mathematically profitable hands to push based on your position, your hand and your chip count.