Hepatitus b

i donated blood last year and got a report saying that i "had a positive test for hepatitis B virus antibody (HBc antibody).
i tested negative for hepatitis b surface antigen but positive for hep b core antibody. i have no clue what any of these mean, and i want to know whether i can infect someone else with it and if so, how, exactly. more specifically, can i infect someone by sharing food/drinks, i.e, through my saliva?
i know that i felt sick before and had symptoms of hep b before, but now i feel totally fine. what does that mean? please explain...