What is the driving force behind the evolution of the 14 species of finches on the Galapagos?

food supply

Climate, terrain, food supply, predators, gene pool, disease, isolation.

Well its an example of adaptive radiation where you have many related species but living in different niches.
The cause for it on the Galapagos is that a few members got to the islands ( which are islolated) and found many "gaps" in the habitats as islands will be under represented in many species/groups and therefore leaves gaps that new species can adapt and evolve into over time. The finches had many different habiats open to them and they gradually moved into them. This was mainly based on food souces eg berries, insects, hard shelled nuts etc
The result is few genera, but many species.