With a closed-sealed headphone (almost) no sound comes out of the back except sound that gets-through the case and earpads. Similarly, sounds from the outside are blocked from your ear, except again some sound leaks through.
An open headphone is completely open on the back and sound comes into the room from the back-side of the driver (speaker). You can hear outside sounds around you almost like you aren't wearing headphones, but the sound does have to go through the driver cone, etc., so it is slightly reduced. Of course if you are listening to an open headphone loud, outside sounds will be masked (drowned-out).
Semi-open is in-between.
...You MIGHT choose a semi-open headphone if you don't care if you can hear sounds around you or not, and you don't care about people around you hearing your headphones, but you like the sound of that particular headphone.