To "work off" something means to work hard in order to make something go away. This phrase is used to talk about just a few subjects. One is getting rid of fat or weight by exercising:
I need to work off about 15 pounds before beach season!
Why don't we go for a little walk after dinner to work off some of those calories.
The other situation to use "work off ___" with is a debt or obligation:
It takes some graduates over 15 years to work off their college loans.
They have their way into the country paid for, and then have to work it off doing cheap labor.
In addition to "work off ___", you can also use "work __ off". The word that goes between is usually something like "it" or "them":
How long did it take you to work it off?