How does Android Market DRM work?
There are two types of protection offered by the Android Market.

The original copy protection is now deprecated and is apparently fairly easily circumvented.

Google now recommends that developers implement its licensing service, which requires a bit of effort on the part of the developer.  It requires Internet connectivity and checks whether the Google Account being used on the device has legitimately purchased the app.  How often the app goes online to check the licence is up to the developer.