The general definition: peptides are "amides derived from two or more amino carboxylic acid molecules (the same or different) by formation of a covalent bond from the carbonyl carbon of one to the nitrogen atom of another with formal loss of water." And "the term is usually applied to structures formed from alpha-amino acids, but it includes those derived from any amino carboxylic acid". [1]
The definition usually used in biochemistry: "a peptide is any compound produced by amide formation between a carboxyl group of one amino acid and an amino group of another. The amide bonds in peptides may be called peptide bonds. The word peptide usually applies to compounds whose amide bonds are formed between C-1 of one amino acids and N-2 of another (sometimes called eupeptide bonds), but it includes compounds with residues linked by another amide bonds (sometimes called isopeptide bonds)." [2]
References:
1. G. P. Moss, P. A. S. Smith and D. Tavernier. Glossary of
class names of organic compounds and reactivity intermediates based on
structure. Pure. Appl. Chem. 1995, 67:1307-1375 (LINK)
2. International Union of Biochemistry. Nomenclatures and
symbolism for Amino Acids and Peptides. Pure Appl. Chem. 1984,
56:595-624 (LINK)