If you want a really general answer, a triple integral represents the area under beneath a function which represents the area beneath another function which represents the area beneath another function still.
Triple integrals aren't all that common in my experience but a more specific case would be something like a problem where an object's acceleration is not constant and is expressed in terms of time. The triple integral of the rate of change of acceleration would yield an expression for the object's displacement in this case.
Where a is acceleration and s is displacement. This is a very specific case though, as I said earlier, a triple integral's meaning depends on what the meaning of the expression being integrated is.