The terms open and closed refer to the area around the back of the sound producing headphone driver. In an open headphone, the area behind the driver, pointing away from your head if you are wearing the headphones, has holes in it exposing it to the air outside, allowing air and consequently sound in and out. The most common example you will see of an open headphone is actually the iPod earbud, or indeed any other common earbud. If you look at the back, you will see little holes, and if music is playing, you will be able to hear it somewhat through those holes. The advantage to this kind of design is that it reduces/removes reflections/resonances created behind the driver which negatively impact the sound of the headphone. The disadvantage is that firstly sound leaks out so other people can hear some sound when you are listening, and secondly you can hear the sounds around you entering your ear through the holes into the headphone. A closed headphone does not have these holes, and is therefore sealed from the air outside the headphone. This means that sound produced by the back of the driver resonates in the small closed box that comprises the headphone, causing some degredation of sound quality, but allowing isolation both from other people hearing your headphone, and from you hearing them.
If someone else can say that more accurately and siccinctly, please help me out!
