Events can become dependent when conditioned on another event. For example, any two dice rolls are independent. However, if we condition on the event that the sum of two dice rolls is 7, then the second roll is no longer independent of the the first roll. Knowing the first roll means you know exactly what the second roll will be, these are now conditionally dependent events. We say events $A$ and $B$ are conditionally independent if $P(A \cap B|C) = P(A|C) * P(B|C)$. Note this is the same as general independence but each term is conditioned on C.