English is not my native language. I've done a test - International English Language Test System (academic), and scored 8.5 out of 9. These are my suggestions (mostly grammatical):
subj:
The term PVP appeared for convenience. It allows to make distinction between the play of humans against AI (this is called PvE) from the play of humans against other human players. This division of terms became inevitable for the clear division of the play against other players and against surrounding AI mobs. [strike]Mostly[/strike]
Most often this term is used in MMORPGs and computer games.
There are several kinds of PvP systems, depending on rules and abilities. [strike]Thus[/strike] In some games there are unique conditions to play against other real players, i.e. duels or arenas, and the game itself may not contain any other PvP elements. The[strike] most good [/strike]
best example of such type of [strike]games[/strike]
game [strike]can[/strike]
would be Everquest II.
Some MMORPGS have [strike]also so-called[/strike]
a flag system, [strike]according to[/strike]
in which the fights between the players may be held in different parts of the game world, except the special areas (cities). In such system the player beginning PVP gets the «flag» (for example, when hitting another player), the color of his nickname changes or a special symbol appears, showing that this player is ready for PvP. If the victim does not respond to such a call, and the player continues to hit and kills him, the player becomes a PK.
I would suggest to to write out the abbreviations when first used.
Edit: Forgot to mention - I'd use lower case v in PvP, but I've seen it used in all caps as well and think you could use either. But imo it needs to be one or the other.