Damping is the setting that adjusts how the tail of a reverb decays at different frequencies. In most cases it relates to high-frequency decay, and its value changes whether the tail sounds bright or dark. In real spaces, air, walls, curtains, and people absorb high frequencies too, so natural reverberation decays at different rates at different frequencies.
Shaping high-frequency decay
Stronger damping makes the highs die away sooner, tending toward a soft, dark tail. Weaker damping lets the highs ring on, giving a bright, sparkling impression. On songs with a lot of vocal sibilance or cymbals, check whether an overly bright tail sticks in your ears.
How it differs from decay
Decay sets the overall length of the tail, while damping affects the color and the frequency balance of the tail. With the same decay time, a faster high-frequency rolloff gives a calmer impression. Damping helps when you want to keep the tail but tame how it hits the ear.
Damping versus EQ
You can also cut the highs with an EQ after the reverb, but damping can affect the change as the tail continues. Since implementations differ by unit, listen for what each one does before making large moves with both at once. Unwanted low end is better handled separately with EQ or a high-pass filter.
Approaches by source
On vocals you might keep clarity while taming harshness, and on piano you might darken the tail to make room for the accompaniment. The right value depends on the source and the song. A setting that feels dark in solo can be just right in the full mix.
Steps for adjusting it
Set decay and reverb amount roughly first, then listen for whether the tail is too bright. Add only as much damping as you need and find the point where it does not clash with the highs of the dry sound. The basics of reverberation are explained in the reverb article.
