A ko (Japanese: コウ, , kō, literally aeon) fight is a tactical and strategic phase that can arise in the game of go.
The existence of ko fights is implied by the rule of ko, a special rule of the game that prevents immediate repetition of position, by a short 'loop' in which a single stone is captured, and another single stone immediately taken back. The rule states that the immediate recapture is forbidden, for one turn only. This gives rise to the following procedure: the 'banned' player makes a play, which may have no particular good qualities, but which demands an instant reply. Then the ban has come to its end, and recapture is possible. This kind of distracting play is termed a ko threat.
If White, say, chooses to play a ko threat, and Black responds to the threat instead of ending the ko in some fashion, then White can recapture the stone that began the ko. This places Black in the same position that White was formerly in: Black can choose to give up the ko, or to find a ko threat. If Black and White alternate making ko threats with recapturing the ko, they are having a ko fight.
Eventually, one of three things will happen.
Before deciding to start a ko, it is worthwhile evaluating what threats are available to both players, so that one can decide which side is likely to win the ko fight. Many of the playing skills come together in ko fighting (evaluating the value of moves; reading ahead to find likely moves of the opponent and best responses; choosing the best order of moves), and it is a topic of much discussion among players. This also causes many beginners to be fearful of fighting a ko, since they are not confident of their ability to evaluate threats.
The importance of a ko varies dramatically depending on the positions of the two players. Some kos offer very little gain for either player, such as three points or less. Others control the fate of large portions of the board, sometimes even the whole board, and the outcome of those kos can determine the winner of the game. For this reason, finding and using ko threats well is a very important skill.
(Copied from http://senseis.xmp.net/?KoThreat.)
Before the fight
(especially local ko threats (see an example of removing a local threat), and double ko threats, meaning they work as ko threats for both sides).
During the fight
If you will lose the ko, you want to get the most you can in exchange for it.