The terms overdamped and underdamped apply to upright pianos only. Overdamping is where the dampers are above the hammers, near the top of the strings. This method of damping is not as effective as underdamping, and the notes on an overdamped piano often tend to ring on even when the key has been released.
Underdamping is where the dampers are below the level of the hammers. The dampers are near the middle of the strings and so the damping is quite effective. This arrangement usually gives a nice, clean note cutoff once the key is released.