Monster Manual 1 states:
Burrow [Movement Mode]: A monster with a burrow speed can move through loose earth at the stated speed and move through solid stone at one-half its burrow speed. A monster can't shift or charge while burrowing.
A monster can't be seen while it's burrowing, but it can be heard with a successful Perception check (opposed by the monster's Stealth check).
Because a Stealth check can only be made at the end of a movement, presumably a creature with burrow can end its movement burrowed underground, making the mentioned Stealth check. However, once movement ends and the creature is still burrowed, what actions can it take? It cannot shift or charge, but can it jump, attack, or use powers?
See this closed question for prior discussion on the topic of burrowing.