Yes it is normal, 24 hours to 48 hours after a hard workout, most people begin to experience soreness in the body parts trained. This is called Delayed Onset Muscle Soreness, or DOMS
DOMS is caused by tiny microscopic tears that occur in the muscle as a result of high intensity exercise (such as weight training, intense cycling, etc). After the workout, the muscle begins to rebuild itself (provided it is allowed enough time and nutrients to recover). This is the rebuilding process which creates new muscle that is bigger and stronger than before. In other words, your muscles are growing. Your muscles grow when you are at rest – not when you’re at the gym.