Infections
Injuries
Inflammatory disorders
Certain drugs
Certain leukemias

The most common cause of an increased number of neutrophils is

The normal response of the body to an infection

In many instances, the increased number of neutrophils is a necessary reaction by the body, as it tries to heal or ward off an invading microorganism or foreign substance. Infections by bacteria, viruses, fungi, and parasites may all increase the number of neutrophils in the blood.
The number of neutrophils may rise in people who have an injury, such as a hip fracture or burn. Inflammatory disorders, including autoimmune disorders such as rheumatoid arthritis, can cause an increase in the number and activity of neutrophils. Some drugs, such as corticosteroids, also lead to an increased number of neutrophils in the blood. Myeloid leukemias can lead to an increased number of immature or mature neutrophils in the blood.
A high number of neutrophils may not cause symptoms. However, people often have symptoms of the disorder that is causing the increased number of neutrophils.