If you multiply it by the probability of A to happen, you'll have the probability :
- that A happens
- that B happens, since you suppose B happens if A happens
So that's why basically P(A and B) is P(B|A)P(A).
Maybe it helps to see it this way, dunno...
Imagine you have a soccer match. Teams A and B have the same probability to score (0.5). A player from team A scores (event A). This will make the players of team A very happy and they will be less careful. On the other hand, players from team B will do their best in order to score back, otherwise they'll be fired by their coach. So given the fact that team A scored first, the probability for team B to score (event B) will be superior, for example 70% !!
These 70% are the probability of "B given A".
And we have P(A)=0.5, P(B|A)=0.7
My explanations in English are just awful so if you have any questions...