A Treasury futures contract is defined on a hypothetical 6% coupon bond. Real bonds have other coupons and maturities, so the exchange publishes a factor for each: roughly the price the bond would have if it yielded 6%, expressed per dollar of face value. The short who delivers receives the futures settlement price times the factor, plus accrued interest.
Bonds with coupons above 6% get factors above 1.0, those below get factors under 1.0. Because the factor is frozen at 6% while the market is not, the equalisation is imperfect, which creates the cheapest-to-deliver effect.
Example: a 4.25% note maturing in nine years has a conversion factor near 0.8700. If the futures contract settles at 118-00 (118.00), the invoice principal is 118.00 x 0.8700 x $1,000 = $102,660 per contract before accrued interest.
Related: cheapest-to-deliver, treasury-futures, invoice-amount, zb, delivery-differential