Pumping is when you can hear the volume going up and down due to compression.
The people at Waves describe it like this:
Pumping
I bet as a kid you tried playing with the volume control of the radio to the music. The compressor does that - except like a dumb machine. The results may remind you of your childhood, may be worse, may be "wow" or may be simply "disappointing". When you can hear the volume jumping around it is called PUMPING - sometimes this is great, sometimes its fashionable (1993 in the US) but it is usually better avoided because it annoys most listeners. Generally caused by a fast ATTACK, a RELEASE roughly in sync with the tempo, a hot drum mix, and over 6 dB of compression or limiting. Perhaps the easiest way to get a compressor to "pump" is to break all the rules, use the worst settings and make the compression as audible as possible - the sound you are looking for won't be far from that setting.
here's another nice one (off topic):
Squashing
Sometimes we hear the compression as a constant intense unrelenting texture. No dynamics, no changes, just 100% loud. This is called "Squashing". We also avoid using a compressor this way most of the time because it can be as annoying as pumping. If you want that effect, start with the tracks - the music, then mix it hot - and if you still need the compressor for more - fine but don't expect the compressor to suddenly make you a killer engineer. The mixes that end up sounding loudest, and translating best to radio & TV are moderate levels with good musical dynamics (compression not obvious). However, the VU meters show a consistent level and the needles strangely don't move as much as the music would hint at. In other words it looks squashed but doesn't sound squashed. Most of the trick is done in the mix - not the compressor. Compressor squashies are usually caused by fast ATTACKS and RELEASES and helped with high RATIOS and low THRESHOLDS. One sees a lot of dBs on the GAIN REDUCTION METER and probably a fast dancing display. Some people assume this is the goal of compression from reading magazines and ads or trying to think "technically". The real goal is to help the music or program - not ruin it. Remember always use your ears! Dynamics are not the enemy - they are musically interesting events and I bet your favorite music or show has plenty of them.
I hope this is helpful to you.
