What is Index Arbitrage?

Legal Definition
Index arbitrage is a subset of statistical arbitrage focusing on index components.

The idea is that an index (such as S&P 500 or Russell 2000) is made up of several components (in the example, 500 large US stocks picked by S&P to represent the US market) that influence the index price in a different manner.

For instance, there are leaders (components that react first to market impact) and laggers (the opposite). As the index is the weighted sum of all components, identifying leaders and laggers can provide a proprietary trader with the opportunity to take positions in these and make money if he/she believes the laggers will eventually rally on the leaders. The challenge being of course to correctly identify these, and to have the technology to act in the marketplace before the price correction takes place.

Traders buying into stocks in advance of their joining an index and increasing weight will profit from the rise in demand for the stock when the change takes place. This effect is largely due to the popularity of index tracker funds which buy automatically on these events. The arbitrage opportunity is thus a zero-sum transfer of wealth from passive index investors to arbitrageurs. As index arbitrage becomes more common, and when reweightings occur more frequently, the loss to tracker investors increases. The presence of index arbitrageurs is an argument for active investment which is less vulnerable to this exploitation (but however incurs higher management fees) or for simple buy and hold strategies.

Other types of index arbitrage include basis trading, the arbitrage between a current index value (synthetically replicated) and that of its future.
-- Wikipedia
Legal Definition
When index futures are rich buyers keep stocks and sell the futures. When the futures are cheap they sell stock and buy the futures.