What does it mean if P(A|B) = P(A) and P(B|A) – P(B)?

This means that the events ##A## and ##B## are independent.

##P(A//B)=P(A)##

##(P(AnnB))/(P(B))=P(A)##

##P(AnnB)=P(A)*P(B)##

This is the definition of independence of events ##A## and ##B##.