Sol is the Roman sun, an old Italian god of the daylight who was later fused with the Greek Helios and then raised by the emperors into Sol Invictus, the Unconquered Sun whose birthday fell at the winter solstice. The separate feast of Sol Invictus is its own form here.
Modern Practice
Sol is called on at sunrise and at the winter solstice for victory, health and the return of the light. His Roman practice was public and political as much as personal: the sun that cannot be conquered was also the sun that guaranteed the state.