Basically, Google Analytics gives you lots of great and useful information on the visitors to your site. You get to see where they come from, who sent them, how they interact with various parts of your site, and all sorts of other nifty things.
There are other methods of getting this kind of information, but Google is currently the best way, and it is free. If they ever do something to mess up the service, like how they have messed up many of their other services recently, then it will be time to use something else. My heart will go on.
Plus while I was at it, I signed up for my new fancy Google+ account (new social button right up there^), and Google Webmaster Tools. I feel like I had to sign a little bit of my life away as well, but I do want people to find me and I do want to interact with people on their preferred social medias. It could have been much worse. I could have used Gmail.