AbcAb or anti-Hbc/antibodiies to total hbc means that you're either currently infected with the hepatitis B virus or you were infected at some time in the past. You may be currently infected with acute hepatits B, or you're a carrier of the virus, or may be your immune system has cleared the virus. To be sure what your status of hepatitis B infection is, you need to take the hepatits B blood panel test. Then the doctors will check if you've HbsAg, anti-Hbs, the status of your liver, etc. Based on the fidings they will determine whether you've cleared the virus, whether you're acutely infected, whether you are chronically infected, and whether you, eventually need treatment.
I hope you've already cleared the virus, which is mostly the case when you're infected in adulthood. The HBcAb will almost always stay in the blood even if someone clears the virus natually, but that doesn't necessarily mean you're currently infected with the virus or you could transmit it if you've HBcAb.
In short, take the other reliable indicators of the Hepatitis B infection such as HbsAg, anti-Hbs, AbeAg, anti-Hbe, Hbv-viral load, etc.
If you use the search box of this Hepatitis B community for similar issues, you would certainly find lots of useful information about Hepatitis B infection, treatment, living with hepatitis B, etc.
Good Luck!