Everyone gets sore when they exercise. The pain you usually feel the next day comes from microscopic tears in the muscle fiber. The rebuilding of that muscle damage creates larger, stronger muscles. In other words, the soreness isn't just normal -- it's necessary.
Sometimes, however, the soreness seems especially severe and lasts for days. That's probably delayed onset muscle soreness (DOMS). It can be quite uncomfortable, but isn't a serious problem. In fact, it's caused by the same factors as regular soreness -- only worse. It usually happens when you perform new exercises at relatively high intensity, so it tends to hit beginners especially hard. Muscles build up resistance to DOMS with multiple sessions [source: Sarnataro].
Rookie runners who can't shake the burn after a day or two can try some massages or light exercise. Some runners suggest just running some more; that might suppress discomfort and help muscles build up resistance more quickly.