In the game of go, the term "miai" refers to two points which accomplish the same result; if deprived of one, the other must be played. The idea can be applied to real life as well - if you are in a room with another person, and there are two equally good meals laid out, there is no need to race to one or the other. It is fine to just wait until the other person chooses one.

In go, often there are stones which are being attacked, but it's not necessary to respond, because there are two ways to escape. It's safe to wait until the opponent destroys one of the escape routes, and then just take the other.

The way to attack something that's defended by miai is to attack something else simultaneously. So you cut off one escape route with a move that also attacks another group. If they move to save the other group, you can cut off their last escape. And if they save the first group, you can continue the attack against the other.

It's a form of the japanese verb "miau", which means to counterbalance, or correspond.

Japanese Go terms
Pi's definition seems a little vague, so I'll attempt to clarify.

Miai is a Japanese term applied to the game of Go (Wei Qi/Badouk). Two points on the goban are said to be miai if playing on either accomplishes the same task. This is an important concept, because if two points are miai, you don't have to play either of them, until your opponent plays on the other. Whichever one he takes, you just take the other. He can't deprive you of what you're trying to accomplish, although he can play on one of the points as a ko threat or kikashi.

Here is an example of miai. A shape needs two eyes to be alive (see Go node if you don't understand this). The black (x) shape shown below is alive with only one fully-formed eye, because the points a and b are miai to make a second eye. If the opponent plays one, you simply play the other.

...........
.ooooooooo.
.oxxxxxxxo.
.oa.x.x.bo.

The bamboo joint shown below is a commonly-occuring shape that exploits the idea of miai. It cannot be cut apart, because the two interior points are miai for connecting.

......
..oo..
......
..oo..
......

見合い

Composed of the kanji for "see" and "meet", a miai is a formal first meeting between prospective partners in a Japanese arranged marriage. These are extremely common in Japan even today; about 20% of all marriages still begin with a miai, and it's a common theme in dorama or manga that unattached men and especially women approaching 30 are pressured by their parents to go to a miai. Strange as it may seem, the institution of miai was created when the idea that love should play a role when determining marriage partners first became widely accepted during the Meiji era. In earlier times, such matters were decided by the family heads or parents, and the future bride and groom had little influence on the decision.

A miai is arranged by a matchmaker, typically an older women who does this semi-professionally. Interested candidates submit and are given short profiles (age, education, hobbies, a photograph) of potential partners. For those who show interest in each other at first glance, the actual miai is arranged, which is usually held at a restaurant or hotel and attended by both candidates' parents as well as the matchmaker. Everyone does small talk and finds out about each other and the two candidates eye each other more or less anxiously. That's all for now (at a traditional miai, anyway).

If either of the two is not interested in pursuing the process further, they should tell the matchmaker as soon as possible, and no hard feelings will come of it (the rejection should of course be worded politely anyway). Otherwise, a first one on one meeting is arranged, and the prospective couple begins a regular relationship. If they discover any hidden flaws, it can still be broken off without major loss of face, therefore this phase should traditionally last at least half a year. If no problems arise, and both parties agree, preparations for the actual marriage can begin.

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