P(A|B) denotes the conditional probability. Which means the probability of event A given event B. In simple words, P(A|B) represents the probability of event A, considering that event B has already occurred.
Conditional probability also shows that the two events are dependent and probability of event B determines the probability of event A.
If the conditional probability of A given B is equal to probability of event A, as given in question, this shows that event A is not affected by event B or the two event are not dependent because the probability of event A is same both in presence of event B and in absence of event B.