Potentiometers are incredibly useful, whether you're controlling the volume on your stereo or the 'mood lighting' in your room. The problem with traditional potentiometers is the fact that your microcontroller doesn't have an easy way to interface with them. Digital Potentiometers solve that problem by allowing you to control a voltage splitter with digital signals.
Wire it up just like a potentiometer and use serial signals to 'turn the knob.' Another handy feature of digital potentiometers is that because they aren't controlled mechanically, they don't have a pre-determined sweep profile.In other words, depending on the way you write your code the potentiometer can 'sweep' in a linear fashion, a logarithmic fashion, or according to any other profile you like. Digital potentiometers can also be used in conjunction with rotary encoders to consolidate large banks of potentiometers into one 'smart' rotary control.