I think that I get some credentials that can be presented to JSTOR and grants me access the article stored there. I don't about the library's relationship with JSTOR, which has more liberal access policies than some journals and other online resources.
All I need is a graduation year and aluminus card number.
Other universities also offer something similar and I think the people behind JSTOR actually wanted to offer wider access. They may depend on academia for funding and think that those funds would not come if JSTOR was free for everybody.
I also don't know the details of the agreements that JSTOR has with the archived journals, which may preclude free access for the general public. A few people might pay the $$$$ per article charges.