They are structurally important to the cell since they are the basic components of which the cytoskeleton is made, and functionally important since it is responsible for catalyzing reactions in the form of enzymes, have mobility functions, act as signal molecules for the cell and are part of a complex to form receptors for those signals and pretty much most other complicated functions. Due to these reasons, they are structurally complex as well.

Proteins are large polymers of amino acids joined together through peptide bonds to form polypeptides or in other words proteins. This is unclear unless you know what each bolded syllable is.

Amino Acid. Click on link for image credit

First, Amino Acids. Each amino acid consists of a central carbon atom bonded to a;

i-             Carboxylic-acid group (COOH); A carbon atom double-bonded to an oxygen atom and single bonded to a hydroxyl group (O-H).

ii-            Amino group (NH2); This is simply a nitrogen atom single bonded to two hydrogen atoms.

iii-           Hydrogen atom;

iv-           A distinctive side-chain that is unique to each type of amino acid, usually referred to as the “R” group. Thus, amino acids differ only in their side chains.

Amino acids get their name because of the amino group and the carboxylic acid group.

When two amino acids come close together, the hydroxyl group (OH) of the carboxylic-acid, which is polar, attracts a hydrogen atom of the amino group of the other amino acid and in the process, forms and releases a water molecule (See below image). This leads to the formation of a peptide bond which is a covalent bond between the carbon of the carboxylic-acid group of the first amino acid and the nitrogen of the amino group of the second amino acid. When many amino acids are linked together through peptide bonds, they form a polypeptide chain (or proteins).

Formation of a Peptide Bond. Click on image for credit.

Proteins are structurally complex. If you look at one (below), you can only see chaos. This is due to the fact that when amino acids begin to form peptide bonds with one another, they do not line up into a straight linear structure, rather, they begin to spiral and coil due to the interaction of their side chains with one another forming various types of (mostly) hydrogen and (sometimes) sulphur bonds.

Typical Protein. Click on image for credit.

So, in order to understand them, we theoretically unwind them and classify their structure under four different sections;

i-             Primary Structure; where we note the exact successive sequence of amino acids that make up the protein through the direct peptide links between them.

ii-            Secondary Structure; when the amino acids grow in number in the polypeptide chain, they begin to coil and either form an alpha helix (shown in diagram) or a beta-pleated sheet due to the indirect hydrogen links between the R-groups of the different amino acids. Here we discuss the amino acids which are forming those hydrogen links, usually four or five amino acids apart, and take the example of glycine (gly) below.

Protein structure. Click on image for credit.

iii-           Tertiary Structure; as the spiral itself coils and continue to spiral, the R-groups of amino acids from different locations (20 or 30 amino acids apart) in the chain will begin to interact and form hydrogen bonds.

 iv-           Quaternary Structure; here, two or more polypeptide chains will come close and interact with each other forming a dimer (two molecules), trimer (three molecules), tetramer (four molecules, as in above diagram) and so on.

This is a link to a very comprehensive video on youtube uploaded by user Pronerual which will delineate the concept of protein structure clearly.