are they replacements for meals? why do people drink it after a workout

say i'm trying to loose body fat, would it be ok to take even if i dont work out on that day?

they can work as meal replacement, but you need carbs with them, so then you take a carb and protein shake.

After workout you're body needs protein and carbs fast. liquid nutrition is quick, its at the muscle about 30 minnutes after you consume them, while a meal can take like 2-3 hours.
So after you have worked out theres a window of time when all you consume pretty much goes right to the muscle.

Since am trying to lose weight

would it be wise do drink a protein shake after my workout

but not necessarily as a meal replacement more like a cold snack

if it fits within your calorie needs for the day, then yes.