Neutrophils are one of the five types of white blood cells.  Neutrophils provide protection against infections.  They are produced in the bone marrow and destroy some forms of bacteria, waste products and foreign substances by eating them.  Any infection or inflammation will increase the number of white blood cells.
Neutrophils are also involved in the process of breaking down proteins.

NORMAL RESULTS

The normal range of neutrophils in the blood is between 40% to 60% of the white blood cells.

HIGHER THAN NORMAL RESULTS

A higher than normal percentage of neutrophils in the white blood cells may indicate:
Acute infection
Acute stress
Eclampsia (high blood pressure leading to dangerous convulsions in a pregnant woman)
Gout (a disease in which the defective metabolism of uric acid causes arthritis and pain generally in the smaller bones of the feet)
Myelocytic leukemia (cancer in the bone marrow)
Rheumatoid arthritis (a disease causing inflammation, pain and often deformity in the joints)
Rheumatic fever (a noncontagious fever, generally confined to young people, accompanied by joint inflammation and pain)
Thyroiditis (inflammation of the thyroid)
Recent trauma (emotional or physical injury)

LOWER THAN NORMAL RESULTS

A lower than normal percentage of neutrophils in the white blood cells may indicate:
Aplastic anemia
Influenza
Other viral infection
Bacterial infection
Radiation exposure