what day of the week
Used to ask which day of the week something occurs or what day it is today. The answer is a weekday name like 月曜日.
What day of the week is it today?
What day of the week would be good for the next meeting?
What day of the week is tomorrow?
On what day of the week do you study Japanese?
何月 asks which month something happens in, while 何曜日 asks which day of the week.
Compound of 何 (what) + 曜日 (day of the week).