From the website:
Great apps start with strong functionality, add device-focused utility, and finish with an outstanding Windows Phone user experience. Plus you will be able to install the Windows Phone SDK which includes Expression Blend 4 for Windows Phone, Visual Studio Express for Windows Phone and the Windows Phone Emulator. Your ideas combined with great tools - which one of the world's toughest problems will you solve?
Details on registering for the Imagine Cup 2012 can be found here. You've got till the 13th of March next year to submit your Application Summary and SketchFlow prototype, and the final app by the 3rd of May 2012.
And when you finish the app, let us know here at All About Windows Phone!