A Peptide Bond is the type of chemical bond that links one amino acid to another. Peptide bonds create the backbone of a protein. Peptide bonds are a type of covalent bond. A chain of amino acids held together by peptide bonds is called a polypeptide.
Unlike hydrogen bonds, peptide bonds cannot be created or destroyed by Foldit players. Players can use cutpoints to temporarily neutralize peptide bonds, allowing sections of the protein to be moved around freely.
Peptide bonds aren't directly visible in Foldit. The protein's backbone is shown as a continuous tube or line, which is implicitly held together by covalent bonds.
While Foldit works with peptide bonds that have already been created, it's good to have a little background on the subject. The key points are summarized here. See the wikipedia article Peptide bond for more detail.
Peptide bonds are created by bonding the carboxyl group of one amino acid molecule with the amino group of the next. (The amino group is of course the amino in "amino acid", and the carboxyl group is carboxylic acid, the acid in "amino acid".)
In an uncharged state, a carboxyl group has the formula -COOH (that is, carbon-oxygen-oxygen-hydrogen). Foldit shows carboxyls in the charged state, which is how they would normally be found in the aqueous solution inside a cell. In the charged state, a carboxyl is -COO, and has a negative charge.
An uncharged amino group has the formula NH2- (one nitrogen, two hydrogens). Foldit again shows the charged version, formula NH3, with positive charge.
In forming the peptide bond, the carboxyl group loses an O. The amino group loses two Hs. The O and the Hs combine to form H2O, a water molecule.
The first amino acid in the protein gets to keep the all three Hs in its amino group, and the last amino acid gets to keep the O in its carboxyl group.
The same reaction can be described using the uncharged version, in which case the carboxyl loses on OH and the amino loses an H. The results are the same.
Since each amino acid loses part of itself in forming peptide bonds, they're technically not amino acids once they're joined up. The correct term is residue once the bonds have been formed. But "amino acid" and "residue" are often used interchangeably in Foldit.
There are also occasional references to N terminal and C terminal in Foldit. The N terminal (N for nitrogen) refers to the amino group, and the C terminal (C for carbon) refers the carboxyl group. A protein always starts from the N terminal and grows toward the C terminal. The segments of a protein are numbered from the N terminal to the C terminal. The mnemonic "amiNo aCid" can be used to remember the order.