January is named after Janus (Ianuarius), the god of the doorway; the name has its beginnings in Roman mythology, coming from the Latin word for door (ianua) - January is the door to the year....
It originally meant something like first month when there were only 10 months (which is why DECember is the tenth month, NOVember is the ninth, OCTober is the eight etc....) until two more were added...