Pumping is the sound of gain reduction moving more obviously than the music needs.
Symptom
The level breathes with the trigger
Compressor pumping happens when gain reduction and recovery become audible as a rise-and-fall effect. It can be creative, but it becomes a problem when vocals, cymbals, or the whole mix lurch around the kick or bass.
The meter may show deep reduction, slow recovery, or repeated dips that do not return before the next musical event.
Causes
Low frequencies often drive too much reduction
A low threshold, high ratio, fast attack, or poorly timed release can make the compressor clamp down too often. Low-end energy can also dominate the detector and pull the rest of the signal down.
If the processor has a sidechain high-pass filter, raising it can stop kick and bass weight from over-controlling the whole signal.
Fix
Time the release to the groove
Back off the threshold or ratio, slow the attack when transients need to breathe, and adjust release until gain reduction recovers musically. Then level-match before judging the change.
Meter Core helps separate the loudness change from the dynamics change so pumping decisions are not biased by level.