Wii Motion Plus is a peripheral add on to the Nintendo Wii remote.  It is a tiny add-on that connects to the bottom of the Wiimote, similar to how the Nunchuk plugs in and adds functionality when syncing to the sensor bar.  Normally, when you use the Wiimote to play a game, there is a millisecond difference in the response time between pressing a button or doing an action and it being sent to the sensor bar before the game responds.  You do not notice this, because you are playing the game.  The Wii Motion Plus add-on eliminates that response time and makes it quicker to interact with your game via the Wii Remote.

When you use your Wii Remote, it sends a signal to the sensor bar placed above or below your television set.  This signal is what lets the game know your Wiimote is doing something and emulates it on screen.  The better the signal, the better response time you have between the two devices.  This makes playing the game much easier.  Using Wii Motion Plus makes it much easier for the interaction to take place and makes it a more stable connection between the Nintendo Wii and the Wii Remote.  The biggest difference in using the Wii Motion Plus peripheral is that it adds an angular rate sensor which utilizes the rotational movements you make when playing a game.  This means when you act out a motion that might be more complex than just forward, backwards or side-to-side, the Wii Remote and sensor bar know how to process the action more accurately.

Wii Motion Plus only works with games specifically designed for it.  So, if you are playing a video game on the Wii that uses it, invest in it for your Wii Remotes!  Currently, Wii Motion Plus runs about $20 at most retailers.  Games will tell you if they are designed for it or not.  Wii Sports Resort is one such example of a Wii game that Wii Motion Plus was built for.