PVE is short for “Player Versus Environment” or “Player Versus Enemy”. “Player Versus Monster” is a synonym for it, and its acronym is “PVM”. However, PVM is not a common term. The term “Player Versus Environment” or “Player Versus Enemy” refers to a game mode where the player has to face enemies that are not controlled by other players. Rather, these enemies are controlled by the computer itself, with the help of code that the game developers.
A game mode does not have to be completely PVE. Meaning that a game can have both types of enemies, the ones that are controlled by the computer and the ones that are controlled by other players. This is common for MMORPGs where you may have to deal with monsters and other players as well. There are not a lot of first-person shooters that have both computer-controlled enemies and enemies controlled by other players. One example of a first-person shooter that has both is Apex Legends. In Apex Legends you will definitely have to deal with other enemy players, but you may also come across huge spiders and tiger-like animals called prowlers. However, they are in limited maps of the game.
Some games or game modes are completely PVE, despite being multiplayer. For example, “A Way Out” is a completely PVE game that you can play with one of your friends. Another example is the Zombie mode for Call of Duty, which is a PVE only game mode.