The peptide bond is a covalent bond established between two amino acids. But it is not a whatsoever bond... it is a bond that involves the a-amine group of an amino acid and an a-carboxyl group of another amino acid. The term peptide bond is sometimes used generically, when any amino group of one amino acid reacts with a (any!) carboxyl group of another amino acid, and this general use is shrouded in some controversy. In fact, some consider that only when the functional groups involved in the bond are linked to an a carbon, the bond should be called peptide, whereas when the functional groups are in different locations in the corresponding amino acids, the bond should no longer receive this name. I personally also agree that only in the first case it is a peptide bond.
The formation of a peptide bond is an example of a condensation reaction, which releases a water molecule. Therefore, one of the amino acids involved in the reaction will release O and H and the other will release H. Thus, since in the final product, each of the two amino acids will not have exactly the same composition which had initially, they should be called amino acid residues. The peptide bond formation requires energy in the form of ATP hydrolysis, and that is why protein synthesis is expensive from an energy point of view. The reverse reaction (cleavage of the peptide bond) is a hydrolysis reaction and releases energy.
The peptide bond is an amide bond (not amine as often incorrectly named!). From a structural point of view, it is a planar bond, that means, all atoms are located in the same plane.
Indeed, the bond is not a single bond, but it is a partially double bond, since electronic delocalization exists between the nitrogen and the oxygen. As a result, the peptide bonds are confer local structural rigidity in the molecules that have them since they are not single bonds, and thus do not suffer rotation. Therefore, they do not allow conformational changes in that location. As happens with the double bonds, peptide bonds can exist in two different isomeric forms: cis and trans.