The support's role in the early game is to control the flow of botlane in such a way that:
In a winning matchup, you get your ADC significantly ahead, and keep them from getting punished by their ego as much as possible.
In an even matchup, you get your ADC ahead if possible, and otherwise help set up the rest of your team to more easily get you ahead, while preventing your opponents from doing the same.
In a losing matchup, to minimize the amount of loss in both kills and cs.
In general, your job is to give your adc the opportunity to scale into the midgame.
After lane phase, your role is map control and fight control.
Map control mostly means warding, warning, and predicting your opponents.
Fight control depends on what kind of support you're running. It can be crowd control, peeling, tanking, damage, buffing, etc as applies to the support played.
Map control and fight control can happen during lane phase but are less pronounced.