This behaviour is also known as Onychophagia or pathological grooming. It is a chronic condition that can be repetitive and compulsive in nature as with trichotillomania (hair pulling) or dermatillomania or excoriation disorder. It affects both children and adults alike.
The underlying emotions are usually include fear, insecurity, uncertainty, etc. Unlike physical reactions, like a pounding heart or hyperventilating, which can result in the fight-or-flight response, nail biting is a way of “releasing” stress and anxiety because it can may feel as though it is creating a “soothing” effect for the person. This habit can give someone something to do, so to speak. Boredom and frustration can also contribute, a feeling of “doing something” rather than “nothing”. Often there is a connection to a perfectionist personality. Behaviours of this type can interrupt a person’s day-to-day activities and personal interactions, most of all their self-esteem.

Other situations which the nail biter may have include –

Attention deficit hyperactivity disorder (ADHD)
Oppositional defiant disorder (when an individual is defiant and disobedient towards people of authority)
Separation anxiety disorder
Tourette’s syndrome

Genetics

Some studies indicate that if someone is a nail biter they have more than likely taken that on by genetics rather than observation. 

Physical and psychological side effects of nail biting include: 

Damage to the cuticle and surrounding skin; redness and pain
Possible bacterial infection in your nail beds and mouth
Dental issues
Psychological issues with self-esteem, shame, depression
Problems with relationships