Its great for those sites that you care about but may not update on a regular schedule. Lots of people use RSS to keep track of webcomics. Instead of visiting the site and hoping for an update you'd toss it in your reader and when there was an update you'd know about it. Reader also kept track of which ones you've read so you don't see just a flood of every post, just the updates.
For me and my shit connection, I basically can't function without RSS. I like to read a bunch of sites and news but there's no way I can bother going and loading up each one individually, scroll around looking for the stories I want to read. Reader just put them in a nice list in one place, I can quickly scan the headlines to see if it interests me, click it to either read a summary or the whole article (depends on the feed), and if I want to visit the web page the link to it is right there. All in one page load.
What makes this extra shitty is Google Reader became THE reader. Everyone used it and a lost of the others simply shut down. Most readers you see now actually plug into Google Reader! So when it goes so does pretty much everything else. I'm sure some companies will step in to fill the void but that is going to take time and Google only gave 4 months notice. Its going to be a rough transition.
