Due to the large number of atoms in even the smallest proteins it is convenient to separate protein structure as a whole into different levels of structural detail that can be dealt with individually.
Primary structure deals with the amino acid sequence that makes up the polypeptide chain and contains no explicit information on the three-dimensional structure of the protein.
Secondary structure is concerned with the way the polypeptide chain folds at a local level and how nearby amino acid residues interact with one another to form regular patterns.
Tertiary structure describes how subsections defined by the secondary structure are folded together to create an overall three-dimensional shape.
Quaternary structure is the highest level of structure applied to proteins and deals with how aggregate functional structures are built from groups of individual proteins (not dealt with here).