I haven't used git, but I used svn and bazaar (which is similar in philosophy to git), so I can answer you in general terms.
The advantage of the so called distributed version control systems (DVCS) is that the repo and the code are together on your machine, and you are not dependent on a remote repo for operations. Every developer has a "branch", his own copy of the repo to which he commits to. You can commit, revert, check previous revisions, without being connected to the net. Officiality of repository is granted by virtue of human agreement, not technical setup. In svn, you only have one repo, which is _the_repo_ you and all the other people commit to. In DVCS, you commit to your own repo, and another developer to his own repo, and each of you can push his modifications to the officially designed repo when he pleases.
Another clear advantage is that operations in a DVCS are fast, blazing fast. svn becomes incredibly slow when you start having a lot of stuff in your repo. This can become annoying very soon.
On the minus side, DVCS are more difficult to use, but you can use a DVCS as a centralized VCS if you want.