From the tutorial: "... Just about every beginners tutorial for XNA starts off with the same things, making a sprite move along the screen. I'm going to show you how to do the same thing, but over a curved line, more specifically over a Bezier Curve. Curvy behaviour its a pretty neat thing to do for some games. You could set up a Physics engine to solve all movement in you game (a relatively complex thing to do) but for some games this would be unnecessary. For example, if your making a side scrolling shooter with aeroplanes you could very easily make your missiles drop from your aircraft, curve backwards a bit and then speed forward ...".