Component takes a video signal and give each part of it its own wire. Brightness(Luma, Y), and Both color channels(Chroma, Cr/Pr and Cb/Pb). Often times component video is referred to as YCrCb or YPrPB. Component is an analog signal, which means that the image is more prone to noise and crosstalk from other cables.
The only problem with HDMI is that anything that involves it is HORRENDOUSLY expensive. $80 for an HDMI cable is way too common.