Search for the indictment, it's on the web and spells out exactly what he did.
In it you'll find that MIT pays for the JSTOR service and makes most, not all, articles available only to the MIT Community (students, faculty, etc.).
During the time when Swartz was downloading the millions of articles, it tied up MIT's gateway to JSTOR so that MIT researchers were unable to access the information they needed. Swartz spent a lot of time downloading the articles. It wasn't just a few hours JSTOR was unavailable for use by the MIT Community - it was multiple days at a time.
I don't think Swartz should be severely punished - but I don't think he should be let off with a slap on the wrist either. What he did is not equivalent to just getting stuff out of a library.
I was part of the MIT Community for 20+ years. Research is the life-blood of the place. So is obtaining grant money. It's quite possible, due to the long unavailability of JSTOR cause by Swartz's downloading, people may have been negatively impacted - due to info needed from JSTOR - in writing grant proposals. Grant proposals have deadlines. Hopefully nobody missed a deadline because they could access what they may have needed on JSTOR.