Good question! I remember the first piece of fanfic I recieved for the first story I posted anywhere, Heartache. It came about a month after my story was online, which was super exciting for me because I wasn't expecting feedback at all. I don't remember exactly what it said, but it was an email from a girl named Heidi, who went on to become my first online friend after I replied to her and we started exchanging emails. It turned out she was a Brian fan too and liked the same kind of stories I did. She wrote, too, and had a website, so she started hosting me, and eventually I started my site and started hosting her, and then we starting writing together. I guess the fact that we became friends through a piece of feedback shows how much it meant to me.
I don't remember the first piece of feedback I sent, but it may not have been until after I started writing (in fact, it may have been to Heidi, for all I know). I don't think I realized how little feedback most fanfic writers actually get and how much it means to them until I started writing myself. Plus, I was probably a little shy about sending emails to total strangers. It seems silly now, but I was only 14 and paranoid about giving out any kind of personal info over the internet (which I wish today's 14 years olds still were!).
