The primary structure is determined by the genetic information (DNA) of the organism. Even a change in a single amino acid in this sequence can completely alter the protein's shape and function. A classic example of this is Sickle Cell Anemia, where one amino acid in the primary sequence of hemoglobin is substituted, changing the entire behavior of the red blood cell.
Secondary: Refers to the "local" geometry (coils and folds).
Tertiary: Refers to the "global" folding of one chain into a functional 3D unit.
Quaternary: Refers to the "assembly" of multiple folded chains (like Hemoglobin, which has four subunits).