It's being developed by Skip, the development studio who made the poorly-received Giftpia in Japan. Chibi Robo was originally announced to be published by Bandai when it was first shown at E3 2003. Since then Bandai dropped the project, but Skip looked around for another publisher.
Shigeru Miyamoto was disappointed that Giftpia wasn't pushed to its creative limit, but was willing to give them a second shot. With more freedom, help and budget available, Skip and Nintendo announced last year that Chibi Robo was now to be published by Nintendo.
The game is about a family who buy a little robot to do their household chores. You control the robot as you go around making the lives of the family easier. As you grow in importance you will even climb higher up the chain of other robots doing chores in the house, ending up with subordinates that carry out your orders.
The reason for a plug is to power up your robot. You have a limited power supply, and you have to plug yourself in to recharge.
The game might even take advantage of the internal clock, so they go on living their lives while the Gamecube is off.