AUC stands for ab urbe condita (From the Founding of the City)
In 1 AUC, the City of Rome was founded by the brothers Romulus and Remus according to Roman myth. Rome became a republic, and then an Empire, that has given the world an order and culture that has unified all of humanity as a single people.
The Romans themselves disagreed on when Rome was founded, but 753 BC is the most common estimate.
It is used as a convenient (non-religious based) time scale for discussions of alternate histories.