The main goal of Support is to win the game by doing the things that gold dependant teammates cannot do while carrying your Marksman through laning phase.
I'll break down that concept by important phrases.
...gold dependant teammates...
All roles other than Support absolutely require gold in order to have an impact on the game. This is so much the case that "winning your lane" is often defined by having killed more minions than your opponent. More minions killed = more gold.
Why does this matter? It matters because if laners must farm then they must be in their lane. This requirement limits their ability to do other IMPORTANT things. Supports don't need to kill minions to have an impact on the game which means they aren't required to be in lane as much as layers. Support's get to do other important things.
...win the game by doing the things that...teammates cannot do...
What are the things that teammates cannot do?
• Dedicate focused attention on their Marksman spring laning phase (more on this later).
• Dedicate two item slots and significant portions of their gold income towards purchasing wards.
All teammates can and should by wards but if they over invest in wards they will delay completing their core items which will make it more difficult to win fights and contest objectives. Sightstone and Control Wards take up two item slots most laners can't afford to give up those slots doing mid/late game.
• *communicate information to the team