Acids are substances that can donate H+ ions to bases. Since a hydrogen atom is a proton and one electron, technically an H+ ion is just a proton. So an acid is a "proton donor", and a base is a "proton acceptor". The reaction between an acid and base is essentially a proton transfer.
The relationship between acids and bases is more aggressive than the donor/acceptor terminology implies. Bases don't passively "accept" protons; they rip hydrogen ions from acids. Acids don't "donate" hydrogen ions; they surrender them.