Why would I want to kill them when I can farm creeps then?
In most cases, you are better off farming the creeps in lane. But there are times when the Jungle creeps are the better option. For one, they are good to farm when you can't safely kill your lane creeps for what ever reason, such as them being too close to the enemy's side of the map, or someone else is trying to farm them. Also, the Jungle is essentially a 4th "lane", and some heroes can kill the monsters there fairly easily from level 1. If you can safely man two lanes each with 1 person, along with having 1 person in the jungle, your team should gain more XP then the enemy team, and potently more gold too, allowing for a good early to mid game advantage. Also, later in the game, is can be more efficient to farm the jungle creeps then the lane creeps.
They can also be used for a few other purposes. First off, several characters have built in skills that can allow them to control the creeps in the jungle (Chen and Enchantress), and there is also an item that allows you to take control of them too (Helm of the Dominator). One of the Character's, Doom Bringer, has the ability to consume the jungle creeps, and gain any ability they have. Some of the abilities the Jungle Creeps have are Stuns, heals, projectiles, and AoE damage, along with several auras that can give Mana Regen, Health Regen, Speed, Armor, or Bonus Damage.
Anther common use of them is to draw them to your own creeps, the purpose of which is to kill your creeps. The benefits of such a thing are is move the front line of the lane closer to your side, along with denying XP and gold to the enemy. Also, it can also be used to try and stack two creep waves on top of each other, which can be useful for a push, though it is rarely helpful in the early game to stack the creep wave.