Pumping is a riding style were momentum is generated by a combination of weighting/unweighting and turning the board. In recent years lot of kids were pumping waveboards on or streets. The technique has its roots in surfing.
As it mimics surfing, pumping has been adopted to skateboarding decades ago. It is essential for skateboard slalom. But pumping is also used, to skate for distance. With the longboard revival a couple of years ago pumping became popular again. The technique has been perfected. So were the decks, trucks and wheels, that are used now. Now it is possible to go for very long distances by pumping a longboard. Long distance pumping (LDP) was established as an expression for this way of transportation. Nowadays LDP is also used as an acronym for long distance pushing. The construction of longboards built of platforms and brackets allows both pumping and pushing. This is one of the reasons, why distance skateboarding flourishes in a nice. Common formats of competition are 24 h ultra skates, 6 h races and marathons. During the long races, the riders alternate between pushing and pumping to avoid unbalanced stress to certain muscles.
It's difficult to explain how pumping works, is difficult to explain. It's better to take a look at it, i.e. in this video by Vlad Popov:
www.vladpopov.com from Longboy on Vimeo.
If you still want to read about it, you should check the article “How to … Pump? Propelling yourself with turns” by Dan Gesmer. On pavedwave.org you find much info on pumping and distance skateboarding, especially in the forum (sadly there is not much goinig on anymore). Another website on all aspects of distance skateboarding is “Skate further”. On Facebook you can find several groups on the issue, i.e. “Distance Skateboarding Worldwide” and Long Distance Pumping (Skateboarding) LDP.