To be immune to something is to be resistant to it. If you had chickenpox as a child, you should be immune to it now.
The adjective immune comes from the Latin word immunis, which means “exempt from public service.” If you're protected — or exempt — from disease, injury, work, insults, or accusations, then you're immune. Vaccinations serve to make people immune to certain diseases. Being a diplomat makes people immune to certain legal persecution. To be immune to bullying means that you don’t let the bad behavior of your peers get you down.