S&P 500 futures contracts give buyers the right to a basket of the stocks in the S&P 500 on expiration date. Priced at 250 times the index, they're used mostly by institutional investors.
A lot of stock trading is based on what is deemed "fair value" for the S&P 500 futures. Trading in the S&P 500 futures goes on in Chicago for a half hour past the New York close. Even after the Chicago close, the futures continue to trade, albeit thinly, in after-hours CME Globex trading. If, in the morning, the futures are trading much higher than the cash S&P 500, institutions will sell the futures and buy the underlying stocks, giving stocks a boost at the open. If, on the other hand, the futures aren't trading much higher than the S&P 500's close, stocks can go down.