If your accountant tells you that you’re exempt from taxes this year, give him a big hug. He is saying that you don’t have to pay taxes.
The adjective exempt traces back to the Latin word exemptus, meaning “to remove or take out” or “to free”. So if you are exempt, you are free of an obligation that others have to fulfill, such as paying taxes. But you can also be exempt from having to obey certain rules, like seniors being exempt from having to sell candy bars for a school fundraiser.