A proof is a preliminary version of a printed piece — either a digital rendering or an actual physical sample — reviewed and approved before the full print run is produced.
A digital proof catches layout and content errors; a physical proof additionally catches issues that only show up in the real material — color shifts, paper texture, how a finish like foil or spot UV actually looks and feels in hand.
For any print run of real quantity or cost, requesting a physical proof before full production is a reasonable safeguard against expensive surprises once the full batch has already been printed.