I'm not sure I understand what this question is meant to mean, "What does higher education?" sounds like an incomplete sentence, I'd have no idea how to answer that.
"What does higher education do?" still sounds slightly odd but I'd expect an answer like "helps people get jobs".
or should it be "what is higher education?" - a simple question which could easily be answered as "an optional level of education such as college or university".
Yeah, "a higher education" and "higher education" are a little different, but people use "a" more often. "What does a higher education do?" is more emphasis on getting the degree, that is, what does the degree do (for you)? Getting a job, getting whatever know-how, etc. "Higher education" is more about the the institution or idea of colleges and universities itself. "What does higher education do?" is more like what is university for? Educating youth, providing training, etc. Hope this clarifies things a bit