If you've been following the previous entries in this series, you'll have seen how to start to crochet, and if you've followed the instructions you should be able to add another couple of rounds onto your project and end up with something that looks like this:
There are a number of things you can do with these little squares. They're a very traditional form of crochet (and a really good way of using up odds and ends), you can see the kind of thing I mean if you search for "granny square" on flickr. When I was first learning to crochet I made myself a coding blanket that I still love!
Crochet doesn't have to be square and it doesn't have to be traditional - I've seen everything from the subversive (crochet covers on parking meters) to the cute (amigurumi). I'm currently working on (currently in the sense that I've begun and I haven't finished yet, rather than it being truly ongoing) a set of hexagonal string coasters. The idea is that they will tesselate and form either a big placemat to put hot pots on or several smaller cup-sized coasters. They're not radical, but they're not really your traditional granny square either!
I'm sure there are many more uses of crochet in general and granny squares in particular - answers in the comments please :)