A clamp is a certain type of move in the game of Go (Wei Qi/Badouk). It is a special case of the contact play. A move is said to be a "clamp" when it is played directly adjacent to an enemy's stone (contact play), in the case where there is another friendly stone on the other side. Note that there must not be another friendly stone on a third side, or else the move would be a simple atari. Here's an illustration showing a clamp:

.....
.xoa.
.....

With the black stone "x" and the white stone "o" already in place, a black stone played at "a" would constitute a clamp.

Clamps are a strange kind of move, one that doesn't show up very often, maybe one out of three or four games at my level. They almost always require the opponent to respond by playing a nobi (stretch) on one of the two free points next to the stone being clamped, because to ignore the clamp would be to invite an atari by the opponent, which may be a bad idea. The person doing the clamping will then usually take the other of those points, since the clamp is usually only played when follow-up plays at those two points are miai for some sort of purpose (often connecting two groups). So, if White extended up in the preceding diagram, Black would usually play contact underneath, giving the following situation:

.....
..o..
.xox.
..x..
.....

Clamps are most often seen on the second or third lines, played in a situation where ignoring the clamp or stretching downwards would result in the opponent being able to capture the clamped stone; the opponent must therefore stretch up, allowing the person who played the clamp to connect under (since the tiger's mouth formation on the second or third line is connected). Here's an example (edge of the goban marked with ###):

........#
...o....#
.....o..#
.x.2....#
..xo1.x.#
...3....#
#########

(Note that this is a highly unnatural formation, and probably wouldn't occur in a real game, but it serves to illustrate the idea)

Black wants to connect his lonely stone on the right to his stronger stones on the left (which presumably have some way to live). One way (possibly the only way, I haven't read this one out) to connect it is to play the clamp at 1. If White plays at 3, Black will play at 2, and there will be no way for White to save her two stones. So White stretches upwards to 2, and Black plays at 3, forming a "bridge under" and connecting in gote. An attempt to play at 3 immediately would fail (White would play at 1), so the clamp is tesuji for connecting.

Similar uses of the clamp show up as endgame tesujis to squeeze a few extra points out of the opponent.