Suppose the smallest positive value we can represent as a floating point number is `001e-55`, and the mantissa always has three digits. One problem with underflow -- besides that it happens at all -- is that while sometimes the difference between `020e-55` and `019e-55` is unimportant (only 5%), the the difference between `002e-55` and `001e-55` is dramatic (50%), and even worse going from `001e-55` and `000e-55` is a 100% change. That is, the underflow occurs "suddenly".
Consider the following process of putting music onto a CD: every short fraction of a second, the volume of the music is sampled and stored as a floating-point number. As the song fades out, going from `020e-55` to `019e-55` isn't particular important to the human ear. However, as `002e-55` changes to `001e-55`, it is noticeable to the human ear, and as the final lingering note finally fades even fainter, the number stored on the cd changes abruptly from `001e-55` to `0`.
What would be desired is that as we're about to underflow, we postpone the problem by going from `001e-55` to `10e-56`, where we are able to put 56 into the exponent -- exceeding the 55 barrier -- by only using two significant digits in the mantissa and giving up more space to the exponent. This is what gradual underflow is.