Thumping
Thumping is a technique recently made popular in the guitar world by Tosin Abasi of Animals as Leaders; however, Victor Wooten has popularized in the bass world a while back. It uses the thumb to pluck a string for a different tone than picking, slapping, and traditional finger-style. This can be utilized against other techniques to add variety to a phrase, as well as providing its own unique tone.
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Technique
The technique is very simple to describe but quite difficult to master. The stroke comes entirely from the thumb, not from the wrist (like a slap); but all the digits of the them are held rigid (unlike finger-picking). The motion should begin with the thumb off the string, gaining enough velocity to hit the string with a little force, creating a slight percussive thump. The contact should be on the side of the last digit of the thumb, and the motion should carry through the string, so that you pluck it. You should follow-through so that the finger-print part of the thumb should come to rest against the next highest (thinner) string.
That's the main stroke, which is a downstroke. After a downstroke, you can perform an upstroke. You basically reverse the entire motion - the only difference is that when coming back, you'll hit the string with part of the thumbnail instead of just the side of the thumb. This stroke sounds more like a traditional pluck with less thump.
The difficulty of this technique is that it requires some speed and gusto to get the correct tone, but it's hard to develop that speed starting out before you are comfortable with the technique. It takes a lot of work to get to that Ah-Ha! point, and then even more work to bring it up to speed...and even more to be able to mix it against other techniques.
Difference from Finger Picking
The big difference from normal finger-picking with the thumb vs. thumping is that thumping has speed in the thumb before hitting the string, creating a percussive thump before plucking it.
Animals as Leaders - An Infinite Regression Intro
d u x3 d u x3
|--------------------------|--h7-----------------------|
|:-----h9--9---9---9---9--:|:-----h10-10--10--10--10--:|
|--h7----------------------|---------------------------|
th th i m th th i m
There's no pick involved here: two hammer-on's (from nothing), a down-thump and up-thump, then finger pick with index and middle finger. The notes themselves are nothing too special, but each measure's 3 different pairs of note-sounding techniques creates a tonal contrast that gives a kind of rhythm to the phrase, making it quite interesting to listen to.