Facebook thinks the purpose of the Internet is to be The Matrix. A sort of lifeboat or ark for people whose lives must consume no more than a watt or two of electricity and some protein slurry.
I propose that the purpose of the Internet is to create a place for people of intellect to work together to create a greater consciousness for the species, so we can make the changes we need in order to survive, with some purpose beyond mere existence.
So I think the purpose of the Internet is to save our species from self-destruction.
It's the only tool we have whose purpose is not yet fully decided.
And survival is the only problem we have that we must solve.