Like Mashi said, it's oxidation taking place. If you can just skim the brown part off, anything green underneath will be just fine. Like others have said, using lemon or lime juice on any unused portions PLUS putting it in saran wrap (plastic wrap) as close-fitting as it can be to the avocado will also help it from turning brown (less room for oxygen).
Enjoy (we LOOOOOOVE avocado here)!