I believe the anti-HBsAb is positive when an individual has either been vaccinated or infected with HBV. HBsAg and HBeAg (antigens present in the hepatitis virus detectable in blood after infection occurs) must be checked if a person is unsure of vaccination status or infection.
I also believe that once a person is infected, unless they are treated quickly with HBV immunoglobulin and begin series of HBV vaccinations, that they will have Hep B chronically. There is no cure presently, but there are excellent treatment options.
@ wilz14: I suspect that your healthcare provider would have told you if you had Hepatitis B. If you are unsure of your results please contact the healthcare provider who ordered the test. Never be embarrassed or feel like a bother when contacting a healthcare provider, that's what they're there for, good luck!
Yup, you don't have to worry. You're immune. Consider yourself lucky!
Antiboties of Hep-B are present. This usually means you have recovered from Hep B infections and have some immunity, or that you once received the Hep B vaccination and are immune. Antibodies are good!