Mobs are a group of monsters (usually 3 or 4 and Boss Mobs normaly 5).
Killing mobs will gain you experience points, money, items. You might also need to kill them to complete quests. Combat between players and mobs is called player versus monster (PvM), or in a broader sense player versus environment (PvE) (PvE is PvM & PvP, at the same time). Players may attack mobs, but some mobs are aggressive, and may attack players without being attacked.