The advisors' main role is to give advice. (surprisingly ) They're members picked for consistently being able to give good advice and support to members. They're someone you can go to if you need one-on-on advice or support on something. Moderators watch the site and make sure everyone is following the rules, and dish out warnings and sometimes punishments as appropriate when people aren't. You can also go to them (and to the admins) for advice, but they were primarily brought on to keep the peace. Admins oversee the day-to-day goings-on of the site and help keep things running smoothly in the forum proper and behind the scenes. We deal with the most sensitive issues that the staff faces. Some of the admins are also board members for EC's Board of Directors, and thus deal with really top-level issues, with others of us are more like moderators with more tools at our disposal and more responsibilities as a result.
Owen pretty much covered it. There're also a few Chat Mods that you may have seen, and they do what us regular Mods do, but in the Chat room.