A "closed bolt" gun means that the bolt is already forward and latched when the trigger is pulled. In a semi-auto, the shot will open the bolt, eject the empty casing, and close the bolt on a new round.
An "open bolt" means that when the gun is in the firing position, the bolt is - open! Pulling the trigger releases the bolt, which strips a cartridge from the magazine on the way by and fires it when the bolt latches. As it cycles back, it ejects the empty and then (in a semi auto) latches in place.
It's worth noting that the ATF decided that an open-bolt gun was "readily convertible" to full-auto and therefore anything not already on the books is Bad.
(Disclaimer: this is my understanding of it after not knowing the answer and looking it up for myself last week. If someone cares to further or correct my explanation, please feel free!)