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