A pair trade is the taking of a long position in one security together with an equal short position in another that is strongly correlated with it. It is sometimes used to refer to multiple long and short positions that are similarly matched.
The effect of a pair trade is to hedge (though not perfectly) against the effect of market and sector movements, so that the return depends on the difference in the performance of the two securities (usually shares).
A scenario for the use of a pair trade is when two shares that have moved together in the past diverge. Such a divergence is often an anomaly and a pair trade provides a simple, market neutral, way of exploiting the anomaly and profiting if the divergence reverses. This is statistical arbitrage.
The obvious objection to a pair trade is that there may be a fundamental reason for the divergence: for example the shares that have gone up may be those of a company that has taken market share from the one whose shares have gone down.