What does proof mean on a US coin?

Answer 1

Proof refers to a coin that was produced with special care, generally for collectors. Such coins are struck more slowly, and with more force, than coins intended for circulation, and generally are produced on specially polished dies with polished planchets.

Proof is often referred to incorrectly as the condition of the coin - while proof coins are in fact usually in better shape than any circulated or uncirculated coin, that is not necessarily the case. Impaired proofs are proof coins that have damage to the surface, be it cloudiness, staining, scratches or nicks. Since a proof coin is legal tender, it can be spent, so it is possible (although uncommon) to have a proof coin with signs of wear.