I have a question about HD on the xbox 360?

My TV is currenltly running as 1080p which is HD, and When i hook my xbox 360 in it does not show up as HD even though my TV is HD, the thing that confuses me is that it uses the same screen as my cable box does so wouldnt that mean that it could be the same (HD) for the xbox 360? . Why is this and what do I have to do to fix it?