Influence is also a term from the game of Go
). It is very commonly used, but difficult to explain.
The idea is basically this: Go is a game of territory. Whoever has the most territory at the end wins. When a stone is played on the goban (board), it influences the area around it, and (usually) makes it more likely that the points nearby will end up under the control of the person who played the stone. Generally, the more stones there are in a region, the stronger the influence. Certain shapes of stones have more influence than others, and can direct their influence in a specific direction. For instance, a wall (several stones in a row) radiates influence perpendicular to itself.
Learning how to use your influence is crucial in Go. Having a lot of influence nearby can greatly change the balance in a local fight, provided the player knows how to apply his influence.
Every game of Go involves lots of trade-offs of various sorts, but one of the most common is the trade of influence and territory. This generally happens when two players are building walls up against one another, near the edge of the board. The person whose wall is on the outside (closer to the edge) will get secure territory between the wall and the edge, while the person whose wall is on the inside (closer to the center) will gain influence over the center of the board. Here is an example (the corner of the board is in the bottom left, marked by ###):
The corner territory belongs to White (o), while Black (x) has considerable influence over the bottom side of the board; fights there will favor Black (unless White also has strong influence from somewhere else). Whom this favors depends on what other stones there are on the bottom of the board. If it is White's turn, White might consider playing at the point a. This would most likely elicit a Black response at b. White would enlarge her territory by about 3 points, while Black's influence would be expanded. A move like a or b, extending a wall which is up against the opponent's, is called a push. After the a-b exchange, White and Black might continue to push, trading White territory for Black influence, but at some point, one player or the other will decide that it is no longer in his or her best interest to continue the pushing battle and will try something different, or play tenuki (temporarily abandon the local situation and start something elsewhere).