During feedforward or backpropagation, large values may multiply with one another and become bigger and bigger very fast even above the numeric limit of computer, eg. 64bit size. Even without such explosion. Values in the network should be limited, or they carry meanings no more.
Value Flow Vanishing
The same multiple problem as in value flow explosion; however, this time is multiplication with zeros or very small values, and the flow end values will be come all zeros.