Hi Derek,
The rest days are important, particularly when you're just starting out, so you don't get injured doing too much too soon. Sometimes new runners get all enthusiatic (which is great
) but then do more than their body's ready for yet and can end up sidelined for weeks or even months with an injury.
As ADS says, you can do other forms of exercise on your rest days, like long walks or cycling perhaps.
Good luck with the running and I hope you continue to enjoy it! 
edited: for spelling 
Edited: 20/06/2012 at 15:38