For undergrads it's clearly a combination of finishing school, networking hothouse, and social club, with some education thrown in.
For postgrads, it's a long-shot chance at tenure (extremely unlikely unless you're the product of an Ivy, but it's nice to dream) and perhaps some improved job prospects. (Also unlikely, but not as much.)
For universities, it's a cash grab. First they get the fees, then they get the bequests. Also, some education is thrown in.
Considering the age/wealth profile is now heavily skewed to the over-50s, it would make sense for universities to cater more for mature students. Remaking university culture as life-long access rather than here-come-the-teens would break a lot of cultural expectations - but might also be the only way to keep the university model alive over the medium term.