In Spanish, ¿Qué día es hoy? means "what day is today"
here is how you can respond..
Here is an example of real life situation where you might need to know the day of the weeks.
You watch the news, and they tell you the weather of the weeks. You will need to be able to understand what days of the week are in order for you to follow the weather that is being told for that particular day. The following is the video showing the weather and days of the week.