Ramping is a way by which terms can be steady increased over some period of time in a simulation. This is most often done for model forcing terms, principally in order to avoid applying a shock to the model.
To understand why ramping of forcing terms is needed, consider tides. Starting a model with the water surface and velocity as zero everywhere, but with full tidal forcing, is analogous to having a planet at rest, then instantly putting a moon and sun in place, in motion with each other. This large, instantaneous change in conditions (forcing) is what creates the shock, which tends to result in spurious waves being formed. Ideally, one would initialize a tidal simulation with the water surface and velocity at all points matching what it should be at the point in time the model is initiated, given the phase of the tides, however this is not generally achievable. Gradually scaling up forcing terms helps avoid this problem.
NRAMP controls whether ramping is enabled, as well as how many ramping terms there are. This is to permit users to apply different ramping times for different forcing terms. The various DRAMP* terms...