Like many countries, Japan uses a 12-month calendar. The names are very simple. January is literally “Month One”, February is “Month Two”, etc:
一月 = January
二月 = February
However, before the Meiji Restoration (mid-1800s) it was common to use an older 12-month system. These months’ names referenced the weather and the seasons (similar to the French Revolutionary calendar).
In this older calendar, January is 睦月.
睦 = good relationships
月 = month
or, “The Month of Good Relationships”.
The January New Year’s period is the longest and most important holiday in the Japanese calendar. Most Japanese people visit their families with whom they (hopefully!) have good relationships.