Janus gives January its name and is invoked by its two-faced symbolism at New Year.
In Roman religion, Janus was associated with beginnings, transitions, doorways, gates, and passages. He is conventionally depicted with two faces, one looking forward and one backward. That image makes him a natural symbol for New Year celebrations: people look back at the year ending while anticipating the year ahead.
The Roman month Ianuarius, which became January, was named for Janus. Roman calendar reforms helped establish January 1 as the start of the civil year, although the date's importance and the calendar itself changed over time. The modern Gregorian calendar retains January 1 as New Year's Day in much of the world.
Janus is often confused with Jupiter because both are major Roman gods, but Jupiter is associated with the sky and supreme authority. Janus's defining role is transition rather than thunder or kingship.