Mecanum drive is a type of Holonomic drive base; meaning that it applies the force of the wheel at a 45° angle to the robot instead of on one of its axes. By having the force of the wheels be applied at an angle to the robot, you can vary the magnitude of the force vectors to gain translational control of the robot; aka, the robot can move in any direction while keeping the front of the robot in a constant compass direction. The basic robot drive systems like arcade drive, tank drive, or shopping cart drive require you to turn the front of the robot to travel in another direction.
The attached paper describes the algorithm used to control Mecanum drive and its derivation, while the attached spreadsheets provide a modeling program for Mecanum wheels. There are two versions, one for Office 2003 and the other for Office 2007-2010. Use the spreadsheet which corresponds to the version of Microsoft Office you have available. These were created in Office 2010 and have been tested on Office 2007, they have not been tested on Office 2003.