Composite video runs all of your video through one channel. This is typically a yellow tipped RCA cable - the kind you would hook up a VCR or DVD player with.
Component runs three separate video lines that each carry one color, and then they combine in your tv. The colors are typically labeled Y Pr and Pb. To connect that you would need to run three RCA cables, or a triple RCA cable.
Component offers a better, cleaner picture.