How important is knowing opening theory
Opening theory is basically the idea that there is a certain way a game should start. This assumption is based upon the crazy idea that you do not want to start the game at a positional disadvantage. In order to accomplish doing that, some players will figure out what move set they struggle against, and then look up the "book line" for it. Where would you go to look those up? Well, you could start here: on wikipediahttp://en.wikipedia.org/wiki/List_of_chess_openings , but another good place to look is google or a chess engine if you have access to one. As for google, just search "11. e4 e5 2. Nf3"Nf3 and google will show you the name of the opening, and contain a link to wikipedia for that opening's basic nuances.
To me, knowing opening theory is more than just memorization. I do not know all the names, but I do try to keep track of the relevant sets of moves that are considered to be advantageous for the lines that I play.
What major advantages would I gain my studying opening theory
Don't just study opening theory in general. Pick something you like, and study the ins and outs of just that one specific opening. You can move on to another one later if you wish, but do one at a time.
The benefits are numerous. Mostly revolving around the fact that the more of these famous openings you know and are aware of, the more that you will be comfortable transpositioning into them, finding traps, building sturdy pawn structures, and recognizing solid development plans.
Don't wear yourself out trying to learn all of them at first. Pick one that you like, and then go with that. Or pick a player you like, and go with theirs. A couple famous players: Fischer, Kasparov, Tal, etc.