Cointegration is much harder to define in laymans terms without being inaccurate. In slightly more complex terms, if the price series x and y are cointegrated, then there exists some equation y_t = a + bx_t + e_t where the error term e is stationary i.e. it's not drifting and has constant expected volatility.
Rob
What purpose does this serve?
In pairs trading, we want to find some parameter which governs the statistical tendency for two price lines to intersect on an overlay chart or a single price ratio line to revert to the mean of a moving average.