Convergence is enforced by arbitrage. If futures sit above cash near expiry, a trader can buy the physical, sell the future and deliver; if below, the reverse where possible. As time to expiry shrinks, cost-of-carry shrinks with it and the two prices must meet.
When convergence fails — as it did in US wheat around 2008 because of a broken delivery mechanism — hedgers lose confidence in the contract and exchanges change the rules.
Example: with two months left, corn futures at $4.60 against cash at $4.35 reflect 25 cents of carry. On the last trading day that gap should be near zero at the delivery location.
Related: basis, cost-of-carry, physical-delivery, cash-market