For Muscle Endurance:
Creatine is a naturally occurring molecule. In the muscle, it takes the form of Phosphocreatine, which is used to create the energy molecule ATP that is needed for muscle fiber contraction.
Supplementing with creatine increases the amount of phosphocreatine in the muscle, and thus increases the amount of ATP available to muscle fibers.
Increased muscle ATP allows the muscle to work longer and harder.
For Muscle Growth:
Creatine supplementation increases the size of the different muscle fiber types: type I (slow-twitch), type IIA (fast-twitch) and type IIX (very fast-twitch) muscle fibers. This, in turn, leads to greater muscle mass.
Creatine supplementation also allows for greater work by the muscle and as such increases muscle growth factors.
Concussions: It is now thought that creatine supplementation can be supportive in concussion recovery by helping replenish brain energy stores. In fact, it is known that creatine levels in the brain decrease after sustaining a concussion.
As a nootropic: Creatine improves the variability of reaction time. Also, creatine supplementation with vegetarians has been shown to improve memory.