The two circles shown below represent two events, A and B. The area of each circle represents the probability of the event. With no overlap you can see that the probability of one or the other of the two events (the union of A and B) written as P(A ∪ B) is the sum of their probabilities. The union is often described as an "OR" statement. The union is the probability of A occurring OR B occurring OR both A and B occurring simultaneously (their intersection).
Drag one of the circles so that the circles begin to overlap. You will see that the probability of the union decreases because some probability is included in both sets (their intersection). You can also drag the letter for each set to change its size and thus its probability.