An index future should trade at the index level plus financing minus expected dividends. When it trades meaningfully above that futures-fair-value, arbitrageurs sell futures and buy the basket; when it trades below, they buy futures and short the basket. The activity drags the two back together.
This linkage is why index futures lead the cash market: they are cheaper and faster to trade, so new information arrives there first and is transmitted to stocks by the arbitrage. It also concentrates enormous activity into the special-opening-quotation on expiry mornings.
Modern index arb is a latency game run by a handful of firms, and the profitable gap is measured in fractions of a point. Retail traders will never capture it, but they should understand it, because it explains why the fair-value gap at the open is not a trading signal.
Example: S&P cash 5,000, 90 days to expiry, financing 5.2%, expected dividends 0.4% of index. Fair value = 5,000 x (1 + (0.052 - 0.016) x 90/360) = 5,045. If the future trades 5,053, eight points are available before costs, worth $400 per es contract.
Related: futures-fair-value, es, special-opening-quotation, quadruple-witching, equity-index-futures