An open rhinoplasty is a nose job that us done with a small incision for reaching the inner parts of the nose. A closed rhinoplasty is a nose job that is performed without any incision. It should be performed only by plastic surgeons that had specific training in closed rhinoplasty since it's a much more complicated procedure then the open rhinoplasty.
You can find more information about open and closed rhinoplasty and generally about rhinoplasty here:
http://www.cosmetic-md.com/face/rhinoplasty-nose
http://rhinoplasty-procedure.blogspot.com/
http://en.wikipedia.org/wiki/Rhinoplasty

http://www.docshop.com/education/cosmetic/face/rhinoplasty/surgery/

In an "open" rhinoplasty, a small incision is made in the columella, which is the little column of skin that separates the two nostrils. That incision allows the nasal skin to be lifted off of the tip of the nose. That's the only difference between the two techniques. In both open and closed rhinoplasty, many other incisions are used up inside of the nose, but the open technique also has that one little extra incision in the base of the nose.

The open technique has huge advantages over the closed technique, in my opinion. The main advantage is that it is much easier for the surgeon to see and work on the nasal tip cartilages in their natural positions. With the skin lifted up, it's easier for the surgeon to see what needs to be done, and to accomplish those tasks. The little scar heals superbly.

I strongly favor the open approach, but some plastic surgeons get excellent results with closed rhinoplasty, so don't select your surgeon based on the open vs. closed question. Select your surgeon based on his overall skill in performing rhinoplasty.