A useful analogy is to imagine the Tellurian as a huge body of water. Most people move with the currents of reality, floating along on a cushion of their own belief. Some of these sleepers, Hedge Magicians or simply the heroically lucky, learn to dip their hands in and alter the flow, but they can't redirect the river. Vampires and werewolves are predators, fast and agile in the waters of reality, but still confined by the flow of belief. The Mage, however, sees the river for what it is, and can push the water around as they choose.
Paradox is the inertia of 6 million gallons of belief. Mages who change reality with vulgar magic are pushing the river in ways it doesn't want to go, and risk being drowned by the current. coincidental magic uses the flow of reality, rather than fighting against it, and can easily avoid Paradox, but even coincidence can risk paradox if it is unbelievable to the local sleepers.
Practically, paradox is the only thing that stands between a Mage and ruling the world. The world is a dark and unbelieving place, and most mortals can't or won't accept anything outside of their normal expectations. The collective belief of Mortals who don't trust Verbena rituals or understand Iteration X energy weapons drives paradox to stamp down these ripples in reality.
Paradox can take a variety of forms. Backlash, reality directly attacking the offensive mage, can cause temporary, long term, or even permanent wounds, flaws, or oddities. Quiet, a magical form of madness, forces the offending mage to resolve their guilt over disjointing reality. Exceptionally offensive Mages can be catapulted into a Paradox Realms, or hounded by Paradox spirits.
Much like the river, the consensus can be moved over time, making vulgar effects coincidental, or even mundane. The Order of Reason has had much success over the last 800 years convincing sleepers to accept their view of reality.
At the Battle of Naseby on June 14, 1645, Scourge changed forever. Due to the high levels of vulgar magic being used at the time, the Scourge became a purely negative force, punishing any mage who used too much vulgar magic. It became Paradox.