...because you're exposed to the rain for a less amount of time.
The level of "wetness" you reach depends on how much time the rain is falling on you. As long as the rain is falling at a constant rate and at the same size of raindrop (and assuming a person isn't stealth enough to dodge raindrops), how wet you get is simply a function of exposure time - and the number of raindrops that hit you.
Yes, I agree with nucleardream, time is the key, but there will eventually be a saturation point, when regardless of whether you are walking, running , or riding a bike you will be equally very wet, of course the various methods will produce saturation at different rates, but once your there you can't get any wetter.
There are many different factors involved including, your walking or running speed, wind direction, rain speed, etc. Here's a mathmatical model that takes many of these parameters into account.