Supports provide three important functions:
1) Aura item stacking. Aura items are insanely powerful in high-tier play because they help everyone on your team (and/or hurt everyone on the opposing team), effectively providing 5 times the aura benefit in team fights, which is what high ELO is based on. Anyone can theoretically pick up these items, but there are often better items for various other champions to fulfill their roles properly. Supports, on the other hand, should have first slots dedicated to these items. Having a Taric/Sivir who you know is going to take a Starks + Aegis and a Soraka/Jana who you know will take a Soul Shroud + Abyssal Scepter helps everyone on your team immensely.
2) Healing. Not all supports provide this, but it can be invaluable. When two teams are on the verge of a teamfight, there is a lot of long-range harassment going on. The team capable of staying at full health in the face of this is the one that will be able to come out on top of the eventual teamfight.
3) Buffs. Whether these are AOE buffs like Taric and Sivir or single-target buffs like Jana and Soraka, making your team or carry better gives you a better shot of winning the fight.