You can download the following:
- Demos for Xbox 360 games
- Trailers for upcoming Xbox 360 games and movies
- Xbox Live Arcade games
- Themes for the Xbox 360 dashboard
- Gamerpics for your profile
Many of the downloads, including all demos and trailers, are absolutely free. The gamerpics, themes, and arcade games cost Microsoft Points which you have to buy either with a credit card on your Xbox 360 or in retail stores.
All of the downloads are tied to your gamertag so if you need to download something you already paid for again you'll be able to for free.