A Peptide Bond is the type of bond that links one amino acid to another by bonding the the carboxyl group of one molecule with the amino group of the next. Peptide bonds create the Backbone of a protein. Unlike hydrogen bonds, as of the latest version of the game they cannot be created or destroyed by players of FoldIt.
After a group of amino acids has formed a chain, each bound to the next by a peptide bond, the amino acids are then referred to as "Residues." This is because the formation of the peptide bond causes each amino acid (except the first and the last) to lose an OH from one end, and a hydrogen from the other end, which combined form water. What remains of the original amino acid is its residue, the term biochemists use to discuss the individual units within a protein.