| A "shoulder hit" is a particular type of move from the game of Go (Wei Qi/Badouk). It describes any move where a player plays a stone on a point diagonally adjacent to a (usually lone) stone of the opponent's. Contrast with a kosumi which is a similar play next to one's own stone. In the diagram below, the "o" shows a White stone. A Black move at any of the points marked with an asterisk would be considered a shoulder hit.
.....
.*.*.
..o..
.*.*.
.....
A shoulder hit is a somewhat strange move, somewhere in between a defensive contact move and an attacking move. Although the stone is not in contact with the opponent's stone when first played, it generally will become so, because the opponent will usually respond with a contact nobi (stretch), as shown here:
....
.xa.
.ao.
....
If Black (x) has just played the shoulder hit shown here, standard replies for White (o) would be at either of the points marked with an a. There is a proverb that one should "Never ignore a shoulder hit." This is because the points marked "a" are very important, and the first player to play on one of them will generally have the advantage. If White were to tenuki (ignore Black's shoulder hit and play elsewhere), Black would likely snatch up one of those points. Note that, in general, the points marked a are not miai (equivalent), even if they appear to be. In this diagram, they are, but only because there are no other stones nearby and the edge of the goban is not shown. Usually, the nearby situation will dictate which "a" is the better one to play, because choosing which side to block will govern the direction of play. It's also worth noting that because a shoulder hit will generally be answered, it can sometimes be played as a form of kikashi (forcing move).
Looking at examples of shoulder hits on Sensei's Library, it seems that they are most often used as probing moves (force the opponent to choose which "a" to play and and then react appropriately) or as a technique for reducing an opponent's moyo (potential territory). Note that after White plays one of the points marked "a" in the diagram above, Black can respond with a nobi of his own and start a pushing battle. Thus, shoulder hits are good if you want yourself and the opponent to build walls. Here is an example:
....
.xb.
.xo.
..o.
....
Here, White responded at the upper "a" (from the previous diagram) and Black then played a nobi of his own, building a two-stone wall (or iron pillar). White can now continue the pushing battle at "b", but she is pushing from behind, which is generally unfavorable, so she will probably tenuki or try a different tactic.
Also note that the oft-seen san-san invasion is a form of shoulder hit. | 
