When I think of robots I think about autonomous robots. Robots that move around on their own and that do not need interaction with other devices to function. This is a very hard problem to solve but impressive when done well. More commonly robots are remote controlled and may even have sensors around the environment in order to function. Here is a fun video of such a "robot":
If you want to see some other videos of great usages for autonomous robots in your home you should look here. And if you just want a long discussion on what a robot for the home could be I definitely recommend you read this.