Primary: The specific sequence of amino acids that make up the protein bound together by peptide bonds. There are 20 different amino acids, differing due to the variable R group coming off the central carbon and these may be arranged in any order, making up the primary structure. This order is important when looking at how these amino acids are positioned to interact in the more detailed structure levels.
Secondary: Localised folding of the polypeptide into alpha helixes and beta pleated sheets, this level is held in place by hydrogen bonds which form between the amino acid groups. The alpha helix is easily imagined as being a coil shape, whilst the b pleated sheet resemles corrugated iron in an aligned zigazag going back and forth.
Tertiary: This is the 3D structure of the protein, giving it its specific shape which is often essential to its function. For example the active site within an enzyme. The structure is held in place by a mixture of disulphide bridges, hydrogen bonds, ionic bonds and hydrophobic and hydrophilic interactions all of which form between amino acids.
Quaternary: The structure of multiple polypeptides bound together to perform a function. A good example of this is haemoglobin which is made up of four separate protein subunits. These interactions between protein subunits may involve the same bonds as those mentioned in tertiary structure.