take the (day/week) off

This means to not work, to stay home from work. You usually don’t use this phrase when you’re going on a vacation. Instead, you use it to describe staying home from work because you’re sick, because you want to rest, because you have a doctor’s appointment, and so on.

If you know how long you’re going to take off, you can say “take the day off”, “take a couple days off”, etc. If you don’t know how long it will be, you can say “take some time off”:

I think I’m going to take the day off.

I need to take a week off so I can look after my children.