NASA has said that they will not be sending any commands to the Curiosity rover for the next four weeks due to the alignment of Mars, the sun, and Earth. Their fear is that the sun could corrupt commands sent to Curiosity and result in unexpected behavior or damage system components.
The [communications] moratorium is a precaution against possible interference by the sun corrupting a command sent to the rover.
Curiosity will be operating in an autonomous mode, running off of commands sent up before the moratorium went into place. After May 1, Curiosity will be able to send back the results of its testing. NASA won't be completely out of touch with the rover as it will still be sending information back to let researchers know its still alive.
We will maintain visibility of rover status two ways. First, Curiosity will be sending daily beeps directly to Earth. Our second line of visibility is in the Odyssey relays.
You can expect to not receive any Curiosity updates during the next four weeks. After that, the team plans to conduct another drilling to confirm and extend what was learned from a drilling that took place in February.