“Draw in a deep breath.”
You're visiting the doctor for a checkup. The doctor wants to check your lungs. He asks you to breathe in so he can listen with a stethoscope.
Draw in a deep breath.
One of the meanings of "draw" is to pull something. When you "draw in" a breath, you pull air into your lungs.
A "deep breath" is when you breathe a lot of air into your lungs, in one long breath. It's usually good when someone breathes deeply. For example, you might breathe deeply when you're exercising, or smelling a wonderful scent.
The opposite of a "deep breath" is a "shallow breath".