In the World of Darkness, every human being has a single spark of potential. Most people do not know they have this, do not care, and want to get on with their lives as if it did not exist. Some people though, figure out what that spark is. That spark is very important, because sometimes that potential activates, and the normal everyday, average mortal Awakens.
What does this Awakening mean? Well, it can mean a lot of things. It might mean magical enlightenment, the finding of the perfect bit of blotter acid, or the realization of a theory that had been bothering you for years.
In short, you come to a realization. Your belief shapes your world around you. What happens when you force yourself to change your belief?
The world changes.
Most mages do not come to the full realization of this power. Few to none can handle that awesome power with any certainty or clarity. Most cloak this new-found potential in a familiar form, using tools to help themselves along. Some believe that they affect the world through spells and that their Avatar, for others through their connection to the watchtowers. Others see their potential through with chants and ritual, science and experimentation, or even through martial arts. Still others view their perceptions as the true determiner of their reality, and alter those perceptions with drugs, alcohol, or sex.
Mages are these individuals with the power to warp reality for any reason they see fit, at best with great success and the expenditure of mana, at worst, suffering Paradox with disastrous effects and unforeseen consequences.
Consensual reality is made of up the beliefs of sleepers. Mages can either covertly use magick to avoid Paradox or vulgar magic, risking Paradox but affecting reality in ways seen by the naked eye (should a sleeper witness an act).
You can change reality to suit your whims. So can they. You want to fly. They do not believe you can.
This conflict in belief between you and everyone else is called Paradox, and the Consensus (the unconscious beliefs of the rest of mankind) metes out punishment through Paradox.
Paradox can cause your magic to go haywire, cause physical damage to you and the area around you, or even manifest as a sentient entity, intent on making you pay for breaking the Laws of the Consensus. Marauders can even shred reality with their magic pushing Paradox onto surrounding mages.
Mage has nine Traditions, or groups of like-minded mages who work together against common foes, the Technocracy (a group founded on making the world rational, safe, and free of as much of the supernatural as possible), the Nephandi, and the Marauders.
Mage divides magic into nine Spheres, or areas of influence: Time, Mind, Prime, Forces, Matter, Life, Spirit, Entropy, and Correspondence. A mage's ability to manipulate the world around them is called his Arete, which goes on a scale of one to ten, since it requires a complex and detailed system of measurement, just like Humanity in Vampire: The Masquerade.