This is a trope that's very common in old-school video games, especially arcade games and arcade-like games. Basically, when you die, you come back to life... right at the very spot where you died or at least right on the screen, and lose no progress. The thing is, that does not mean that Death Is a Slap on the Wrist. In fact, this design element is most common in games which have a distinct lives limit, and running out of lives could mean starting the level over, or ending the game altogether. Some games have this feature only in the multiplayer mode, but not the single player mode, which instead brings you back to the last checkpoint. Players also have to go back to the last checkpoint if all of them are defeated at the same time. This is sometimes done so that players who are defeated while their friend is still alive can quickly rejoin the action, rather than waiting for the next checkpoint to be reached. Not to be confused with Auto-Revive, which is an item or spell in RPGs that allows you to come back to life on the spot, but must first be obtained or invoked. This trope is instead about a consistent play mechanic.
Examples of games that always let you do this:
Examples of games that only let you do this in multiplayer:
Any more examples? Do We Have This One??