One of the big ones is the jungle provides quite a good bit of XP and Gold. You dont want that xp/gold to just go to waste, or worse go to your opponents do you? Good teams don't typically give away dragon for free, why would they do the same for the jungle.
Also it gives a teammate the ability to solo a lane. While the xp isn't as good as it used to be they can typically expect to hit 6 a lvl or 2 ahead of duo lanes. Thats pretty good. Also they get more last hits than they would if they had to share the lane with someone else.
So not only are you getting a comparible amount of xp/gold as you would in a lane, but you also give your lanemate slightly more xp and almost 2x the gold.
Also it opens up the opportunity to ganking lanes as you are frequently mia.
Teams can win without jungling, but they typically go through and milk the jungle when their lane is pushed to still get some gold/xp from it.