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).
This old system is based on a lunar calendar with exactly 28 days in each month, beginning and ending on the new moon.
September is 長月:
長 = long
月 = month
So literally, “the long month”.
In September the nights get longer, and we can enjoy the beautiful harvest moon. The September full moon sees the arrival of the Moon Viewing Festival, celebrated in many East Asian countries including Japan, in which it is traditional to enjoy the beautiful moon whilst eating white mochi (rice cakes). 🎑