Feed me

Okay so I'm pretty computer savvy. But I cannot FOR THE LIFE OF ME figure out what feeds are!! Like when someone has the little feed symbol or xml thing on their blog and you click on it, and it sends you to this massive page full of text and code and that's it, WHAT AM I SUPPOSED TO DO WITH THAT???

When I want to follow a blog (a recent development since blogs did not used to really be my thing), I just hit the Follow button on the top if it's a blogspot blog, an if it's anything else I usually just save it as a bookmark and forget about it until I'm cleaning out my bookmarks a year later. I use Google Reader to save blogs I like too, but that's another thing I usually misplace. Right now, I could not tell you how to get to my Google Reader.

So anyway, what are feeds?? How does one follow a blog that's not a blogspot blog??? I'm that dense. I even read the wikipedia article on feeds and I still don't get it.