>>10436315experience to level up for better abilities/stats and gold to buy items with, same as killing the enemies minions in lane. the main reason to kill the neutral mobs specifically is just to reap the benefits of not being bound to a lane.
with the character i've been playing for example he does a lot of aoe damage with a very short cooldown ability so he can kill npcs extremely fast but struggles a lot against actual players that can just dodge the ability. as such being stuck in a lane is a nightmare because there's someone there to threaten killing you if you try to kill the minions, but he can outpace most other characters if left alone to farm neutral mobs since he kills them about as fast as they spawn which nets more overall resources than killing minions in a lane as soon as they spawn.
there are characters on the other end though who are so good at fighting people that being in a lane sucks because lanes have towers dotted along them that do huge damage to enemy players if they get in range and any opponent would just hide under that tower for safety instead of ever trying to fight you. these characters will run around killing just a few neutral mobs so that they don't fall far behind then use the fact that areas in between lanes are covered in a fog of war to show up behind people when they're far away from towers to fight them