The term shove has the same meaning as the expression jam or all-in. It indicates an action by which a player wagers their entire stack.
For example, you could hear a player say, I was down to 12 big blinds, and as I looked down at my hand, I saw suited ace in the cutoff, so I decided to shove.
This means that they moved all in, putting their entire stack of 12 big blinds on the line.
There is no real difference between the expression shove or any of the other counterparts used to describe the same action, so it is really down to your own preference for which one of them you want to use in a conversation.