Simple, for many many people it was their first taste of the FF saga. I owned Sega systems including the Saturn so I missed the Nintendo FF years. So FF VII was there when I finally switched to PSone.
A lot of FF VII's love is based on that memory, it also help that it had a good story, good characters, a decent bad guy who who was actually a twisted good guy and for the time it had great graphics. It also had some rare stuff never seen before and in some case still not seen. Until FF VII had come along I had never played a game that had a fairly involved story line. Most games were good guy, bad guy, kill stuff, find bad guy, kill bad guy. FF VII had a story line that twisted and developed the characters they weren't as one sided as most typical games and of course their was the big one. Aeris death cemented something in a lot of peoples' minds. Here was you watching as a key character, who you may have developed and used suddenly being killed and not that fake will turn up at a later point and let you play her again killed, but genuine dead and gone. Something that I had never seen before in a game and not seen since.
Now I haven't played any of the FF games prior to FF VII so there may well be a chance that some of the stuff I mentioned above turned in those games but then we return to my original point being that for a lot of people FF VII will have been the first game in which they saw these things.