Ported; Uses a larger box that has one or more openings in it to allow the sub to continue to move after it hits, making it "pulsate", (think of a guitar string) the free air in the box is the same pressure as the air outside of the box so that there is nothing other than the speaker's mechanics to pull the cone back in.

Sealed; Uses a smaller box that has no openings so that the air inside of the box is a higher pressure while playing. When a subwoofer in a sealed incloseure hits, it hits hard and then the cone is sucked back in by the higher pressure of the box, allowing it to play the tight punchy bass more accurately. But when it comes to music that the bass "rings" after it hits it won't play as well.

There are also bandpass boxes too, I know that they use a sealed box also but go another step further and enclose the area infront of the cones too.
If I have any information wrong feel free to correct me.
From experiance, I know that too big of a box will hurt not only your music but it reduces your sub's life too.

