Ciao Gustavo!
Yes, GitHub is the website for, how can I say, storing in the cloud Git repositories.
Git is an open source version control system made by Linus Torvalds - which happens to be what I use for code management (there are others, like Mercurial, Subversions, etc). You can give it a try here.
For opensource repositories GitHub is free, while if you need private ones you've got to pay a subscription. There are several websites that hosts repositories, I have an account at bitbucket.org (which provides free private repos).
Or you may use Git in combination with a DropBox account - which is handy and what I personally use most of the times - you can find instructions here.
Cheers,
Davide