A refinery that runs out of crude stops earning money. The value of having barrels on hand — of never having to halt production — is a yield that no futures contract pays. When inventories are tight, that yield rises and nearby prices rise above deferred ones.
It is the missing term that makes the carry formula work: fair futures = spot + carry - convenience yield. High convenience yield is the textbook definition of a tight physical market.
Example: a crude curve in $2 per month backwardation despite $0.50 of monthly carry costs implies a convenience yield around $2.50 a month — the market paying up for barrels now.
Related: cost-of-carry, backwardation, storage-cost, forward-curve, basis