I wrote on Quora about how the Wii Sensor Bar works when someone asked whether the Wii Motion Plus required the IR (sensor bar):
The IR bar provides a reference point (two actually) for the remote. Wii motion plus supplements the Wii remote's existing capabilities with a more advanced gyroscope.
Imagine you are in a completely dark room and are trying to find your way around. You know you are being turned around and that the room is moving, but you can't see anything. And everything feels the same. Which is way is up? Where is the front of the room?
Now imagine there is a single little LED light at the front of the room. Now you can figure out where the front of the room is. But you continue spinning. Is the light upside down or right-side up? Based on your currently angle you can't tell. Are you looking at the light from an angle, or are you directly in front of it?
Finally, imagine there are two lights about 1 foot apart. You can draw an imaginary line between them. If that line is horizontal then you know the front of the room is probably right-side up. As you get closer to the lights that imaginary line gets bigger. As you get further away it gets smaller.
This is very similar to the way the IR bar and Wii remote works. Without the IR bar, the wii remote has no idea where the TV is or how far away it is. For anything requiring you to point at something on the screen with the Wii remote, the IR bar is required.
There are actions the Wii Motion Plus controller can take that don't require the IR bar though. If you have simply have to "shake" the remote, the gyroscope in the remote is enough to know that the remote has shaken.
But for almost all actions requiring you to point to something at the screen, the IR bar is required. (Or if your sensor bar is missing, two candles will work too).
Does Wii Motion Plus require the IR Bar? on Quora