[quote name='Xbox.com']http://www.xbox.com/en-US/community/personality/elle/20060814-shoptilyoudrop.htm
Usage Restrictions
So, you've got your content, but one day, you take it to another console, and you notice it seems to work differently than it did before. There's a reason for that, and it's related to licensing and usage restrictions.
When you download content from Xbox Live Marketplace, that content is licensed to the console you downloaded it to and the profile you downloaded it with. The console license allows anyone to use that content on that console, online or off. The profile license allows you to use the content on any console, as long as you're signed in to Xbox Live (the reason you have to be signed in to Xbox Live is that your profile has to be validated with the service).
For example, if you try to play your new Xbox Live Arcade game offline on a different console, you may find that it only plays in demo mode. This is because the console is not the console to which the game is licensed, and your profile can't be validated until you sign in. To play the full version on this other console, you have to sign in to Xbox Live.[/quote]
This is also spelled out in the License Agreement that is displayed every time you download something from marketplace.