As lunboks explained PvP describes fighting among player. There are different versions of PvP that you might encounter within different games:
Duels - this is the lightest form of PvP as it generally requires both parties to agree to the fight and the possible repercussions to your character are manageable. (No lost items or death penalty for example)
Arena fights - Comes in several flavors but essentially all willing participants enter some kind of special map or area to fight (usually in teams). Death penalties and items loss usually applies to this form.
Open Season - Generally you can attack other players at will and may loot their remains when you defeat them. There may be restrictions on what level of players you may attack or other measures to limit griefing. But generally speaking you're fair game...
Usually when people talk about PvP they mean the third kind (maybe second one too) as it does not require mutual consent and it is therefore easier to find opponents/victims.