This term is often used to define technical/sounds in a track especially in electronic music.
Pumping is a technical term which (for the most part) describes the compression technique used.
Having said that, many people mess up this term with various ways, others with sidechain bass compression, or others with simply loud kicking tracks.
Pumping is an effect created when a compressor dives a bit more than what's needed to compress but still remain transparent, so you get to hear the compressor work.
Good pumping, when intended, is moving according to the groove of the song(attack & release times) thus enhancing it(the groove). Many producers go for that effect since electronic music is already overcompressed, they think - well let's get something good out of this - (a bit shallow but could be true).
Keep in mind that it wasn't always like that. Pumping is a relatively new added effect to "The good ones". In the older days when something pumped, most of the time it wasn't that good and that's because pumping often referred to the way some denoisers worked or bad compressors.
Here's a quote regarding the results of dbx denoising process.
The downsides of dbx are several. First of all, some people hear artifacts with tapes processed with dbx. These are usually in the form of signal pumping and gating. When there is virtually no signal present the noise seems to disappear.
So, many engineers, including myself (if I could lend that term to describe me) judge if they like pumping or not, me personally, when it's done right.. I love it. And if you know how to manipulate a dbx correctly, pumping can give some nice touch to the track.
So, before me a lot of engineers started messing around with pumping and some of them started using it to enhance the groove of a track or to make the beat/drums more apparent in a psychoacoustic way.
Imagine 2 same kicks. Without pumping: The kick just plays, in balance with everything else, and everyone can have a clear image of what's going on.. ok cool.
With pumping: The (same) kick drops and momentarily most of the high frequencies dive, and before you've got time to breathe, another kick drops (with the snare) and again the highs are gone, and goes on to create a very strong 4 to the floor feeling. That DutssKatssDutssKatss (mmmhh funny :) ). So bottom line every frequency or effect (like reverb or delay) that makes you feel lighter and let's you breathe is (momentarily) gone, and makes way to create a massive mean beating track and make everyone dance to it :D
So all in all, pumping is an aggressive compression technique used to enhance the groove and feeling of the track. Mostly done over all the track or in some summing point of the mix.
Happy pumping :)