From Pavement Magazine:
Potholes start as cracks in the pavement. These cracks expand and contract with freeze/thaw cycles during the winter, and as cracks expand or become more prevalent, more and more moisture - rain and melting snow - reaches beneath the pavement surface. This moisture weakens the base and subbase; as it loses its strength it can shift when traffic drives over it - and potholes can result.
This process is accelerated as the temperature drops because the wet material expands when it freezes, pushing up the pavement surface. The wet base or subbase contracts when the temperature rises and thaw occurs.
After a number of freeze-thaw cycles, a small space is created between the asphalt pavement and the base. Traffic breaks the pavement into the depression, creating the beginnings of a pothole. The longer the pothole is left untreated, the deeper and larger it becomes and the more extensive the damage to the surrounding pavement. Left untreated, this defect will accelerate overall pavement deterioration. So it is cost-effective to repair potholes as soon as they occur.
But when they do occur there are a variety of ways to repair them, depending on the goal and budget of the client.