I do this and it seems to help get a dying pipe going again, as others have mentioned. I don't know why? On the one hand, it seems to me that restricting the air flow should make the pipe go out. But it seems just the opposite. I've not made any measurements, but have done it enough that I believe the effect is real and not just my imagination.
I do notice that I seem to get more smoke, and hence, more flavor, when I cover my pipe with my fingers.
Possibly, it is a heat transfer problem. Drawing air through the pipe provides oxygen for combustion. But, it also cools the burning ember. For combustion to continue, the temperature needs to be above a certain level (don't know the minimum combustion temperature for tobacco?). So, drawing in air gives oxygen for combustion, but also cools the pipe, which will tend to make it go out? Perhaps, when restricted by your fingers, one gets enough oxygen but limits the cooling, so that the ember heats more, rather than less and burns better?
I'm guessing here and haven't thought about the problem in great detail. Perhaps someone else knows the real answer?