Well, first let's start by exploring the meanings of the verb "to drive": Usually, you use it to express someone "steering a car". But it also has other meanings. The one you're looking at in your example is this meaning:
to drive: Provide the energy to set and keep (an engine or piece of machinery, a process) in motion
example: A turbine driven by steam.
So in your case it means that photosynthesis is a process that provides the energy and the possibility for life to sustain itself.