A polymer is a long chain of much simpler carbon-based molecules. It can be a straight chain or elaborately branched. Most of the molecules that make up our bodies are polymers. They may be made up of only one kind of molecule or of a number of different but similar molecules.
Proteins are straight chain polymers composed of 20 different kinds of amino acids arranged in various orders. The order of the amino acids determines how the chain folds in on itself and thus the final shape of the complex. It is the shape of the protein that determines whether it functions or not. Even one tiny error can cause a protein to adopt a wrong non-functional shape, or no shape at all.
There are many examples of natural polymers. Starch is a polymer of glucose found in plants. Cellulose is a similar polymer found in plant cell walls. Wood is mainly cellulose fortified by lignin, another polymer. Paper is made from wood. Plastic is a polymer, nylon is a polymer. DNA is a polymer and so is RNA.
Spontaneous formation of polymers under natural conditions does not happen. We need living cells to force two smaller molecules into a connected relationship. It takes a lot of energy to force chemical bonds between small molecules to create these connected chains. To form a protein for example, we need a process called dehydration synthesis.
Dehydration synthesis refers to the formation of larger molecules from smaller reactants, accompanied by the loss of a water molecule. Many such reactions are associated with formation of biological polymers. Given that joining two molecules together to release water is a process that requires a lot of energy, it is obvious this is not going to happen out in watery environments such as origin of life scenarios typically propose. The process needs a living cell with appropriate enzymes to catalyze the reaction.
To link two amino acids together, each with the basic formula H2N-CHR-COOH, a hydrogen atom from the amine group (H2N) of one amino acid reacts with the carboxylic acid group (COOH) of another amino acid to form an amide bond that links the two amino acids in an amino acid dimer and releases one molecule of water (H2O):
[Thus from H2N-CR-COOH and H2N-CR-COOH an OH is removed from the first molecule and H from the second (making H2O) thus linking the two amino acids in an amino acid dimer.] (R stands for different radicals that represent other constituents in the amino acids).
Through this process a complex molecular machine in the cell called a ribosome links amino acids together to manufacture proteins according to the information mandated on a messenger RNA molecule. A similar dehydration process is used by cells to form sugars into the polymers of starch, cellulose and glycogen.
Decades of experimental studies have demonstrated that biological polymers cannot form in natural settings apart from the living cell. Origin of life research has never been able to overcome this problem.