What is "orthomolecular" ?  What does the "orthomolecular" in "orthomolecular science" mean?

"Ortho" is a Greek word that means "right".
"Molecular" refers to the smallest unit that is not an element; it refers to the smallest compound.

So, "orthomolecular" refers to a "right molecule".

An orthomolecular substance is something that provides the body with the "right molecules" it needs for health.  It might be called "optimal nutrition". 
 
Linus Pauling coined the term "orthomolecular" 

As for the word "science", the dictionary definition of science, as quoted from the Merriam-Webster online dictionary, [1] is the following:

1: the state of knowing : knowledge as distinguished from ignorance or misunderstanding2 a: a department of systematized knowledge as an object of study <the science of theology> b: something (as a sport or technique) that may be studied or learned like systematized knowledge <have it down to a science>3 a: knowledge or a system of knowledge covering general truths or the operation of general laws especially as obtained and tested through scientific method b: such knowledge or such a system of knowledge concerned with the physical world and its phenomena :

[1]  merriam-webster.com/dictionary/science

References

             From Orthomolecular Science to Orthomolecular Medicine


The practical application of orthomolecular science is orthomolecular medicine.

Orthomolecular intervention can help in the regaining of health.  It can be used to therpeutically treat diseases such as cancer and AIDS, or to help prevent the progression of degernerative diesease and aging.  Orthomolecular medicine is occasionally referred to as megavitamin therapy.

Orthomolecular medicine holds that larger than usual doses of certain nutrients can actually prevent or cure disease. Although there's still considerable debate over specific dosages and their therapeutic effects, the basic principle is now firmly established and widely accepted.[1] Orthomolecular medicine focuses on the role of proper nutrition in relation to health. Nutrition is first on the list when it comes to diagnosing and treating.  In this respect, orthomolecular treatment is really a small percentage of total medical care rendered in North America. Most people with health disorders who go to their physicians are likely to receive a variety of drugs.

Orthomolecular medicine, while generally harmless, can be dangerous if safe doses of nutritional supplements are not observed. Some supplements, such as vitamins A, D, and E, can build up and cause undesirable consequences.[2] 

Orthomolecular medicine believes that the basis for health is good nutrition. It uses nutrients and normal (''ortho'') building blocks of the body in optimal amounts as the basis of  treatment. The objective is touse the amounts that lead to the best health and greathest decrease in disease.   It is the most effective prevention in the treatment of disease.

Orthomolecular medicine might be considered when Down syndrome is present. [3] Orthomolecular treatment for alcoholism involves using the nutrients necessary to overcome nutritional diseases caused by alcoholism.

[1] worldwidehealthcenter.net/directory-44.html
[2] altmd.com/articles/orthomolecular-medicine--encyclopedia-of-alternati
[3] warnerhouse.com/orthods.htm