Map visibility is essential to winning games for several reasons:
1) It prevents ganks. If you know the enemy jungler is sneaking up on you, then you'll know to stay back. Life=saved.
2) It allows you to control your own buffs. If you have good map awareness, you can catch the enemy jungler trying to steal one of your buffs. You can then gank the jungler, netting you a kill and also setting him or her way back on their jungle.
3) It allows you to counter jungle effectively. If you see the enemy jungler messing around on the other side of the map, then you know you're clear to steal their red or blue buff. Getting that extra buff is huge because then you (assuming you're the jungler) can give your mage or carry your own blue or red buff respectively. that way your team has two buffs while their team has none.
4) It can tell you when the other team is doing dragon/baron. Baron and dragon are both essential objectives for winning the game. Dragon gives your team significant gold, and baron gives an incredible buff that can be absolutely game changing. Without proper ward coverage, the other team could go in there and steal it without you knowing. Furthermore, you won't even get a timer on them, so you have no idea when they'll respawn, possibly costing you baron number 2.
5) It can help you get drag/baron. If you can see the other team on the wrong side of the map, then you know it's safe to do dragon/baron. If you can't see them, then they could be around the corner, waiting to attack in the middle of your baron/dragon fight, probably winning the ensuing teamfight and taking baron/dragon for themselves.
6) It allows you to gank. If you can catch an enemy team member out of position with a ward, then you can gank them and pick up a free kill.
So yeah, wards and map awareness are really important :D. Hope that answered your question.