night of the full moon; 15th night of the 8th lunar month
Refers specifically to the full-moon night of the 15th day of the 8th lunar month (around mid-September), a traditional moon-viewing festival. Often associated with offering susuki grass and dango.
This year's harvest moon night is on September 15th.
We decorate with pampas grass on the night of the full moon.
十五夜 refers to the night of the 15th (often the harvest-moon night itself), whereas 名月 names the moon seen on that night.
十五夜 refers to the night of the mid-autumn full moon festival, whereas 望月 can refer to the moon itself on that night.
From 十五 (fifteen) + 夜 (night), referring to the 15th night of the 8th month in the old lunar calendar.