Why do squirrels cut down tree branches?

The lawn is covered in largish tree branches all of a sudden. My friend is guessing oak, I'm guessing maple or linden. It happened at dusk. We observed several squirrels running around up in the trees, and wonder why they cut down so many fresh branches. Do they drink the sap? Collect and use the branches later to build new nests or fix old ones? My friend said there weren't any nuts, or remnants of nuts. Why do the squirrels do this? (Late June, New Jersey.)