Open --- Closed is actually what it says on the tin
Open headphones have the driver 'open' to the outside world, like my
Sennheiser HD600. Just an example, I need to have my iPod just off full to drive them at a good volume as they are intended for home use. My
ESW9 are
closed.
Open headphones means that you will hear more of the outside world, and people around you will also hear more of your music. Closed headphone offer isolation for both you and people around you
Done well, both designs can produce excellent sound. Some people say open design has a larger sound stage which closed cannot match but its all for debate, as for example the Denon D5000 is one of the highly regarded headphone out there and is closed design
That is why I suggested if you go for full sized headphones (that you wear over your head), to go for closed as you do not want masses of sound to leak out
In-Ear earphones are just that and are only about portability and isolation. Having spent too much of my student loan on this hobby I will say £ for £, IEMs cannot match full sized headphones for sound quality, but then I have not tried the latest round of top range universal IEMs