What exactly does it mean to have eosinophils which is higher than normal range?

How high?: An eosinophil count slightly above normal may be due to allergies, asthma, reactions to medications, certain infections, etc. A very high count (>1000 or so) for several weeks to months could be a sign of disorder of the immune system or bone marrow, or certain parasitic infections. Talk with your doctor about your symptoms, and see a hematologist or immunologist if your counts are very high.