On a grading plan, the existing-grade surface and proposed-grade surface together define the soil that needs to be moved. Wherever existing is above proposed, the contractor cuts; wherever existing is below proposed, the contractor fills.
Net cut and fill (cut volume minus fill volume) tells you whether the site balances. Positive net means surplus cut to haul off-site. Negative net means soil has to be imported. Designers usually try to balance the site close to zero to minimize hauling costs.
Cut and fill is measured in bank cubic yards (BCY) for the in-place state, or loose cubic yards (LCY) after excavation. Hauled volume uses LCY because trucks measure the loose state. Apply a swell factor to convert.