"Doctor, Doctor will this ointment clear up my spots?"
"I never make rash promises!"
Ointment is liquid that you put on your skin if you have a medical problem with it.
To clear up here means to make something better.
The joke lies with the meaning of the word rash. Rash normally refers to a problem with your skin because of an allergy etc. Rash also means a risky decision or statement made before enough time has been taken in making that decision or statement. When the doctor says I never make rash promises, it can mean she doesn't make promises about skin problems or she doesn't make promises too quickly. Clever, isn't it?