The result of a CBC shows that my 8 year old daughter has high monocyte count which is 12.7 and her hemoglobin count is 151. She has been having fever for 2 nights already which usually occurs in the evening or at dawn. What does this indicate?

Could be virus. That level of monos is not worrisome. A virus can cause the fever and many can cause mild elevations of the monocyte count. Her hemoglobin is fine. I would have her rechecked if the fevers continue for more than four days.
Agree with Dr. B. Her lab results are not a cause for concern. If she is eating and engaging in her usual activities, it is likely a transient viral infection. Make sure she drinks enough water so that her urine is mostly colorless. You may use acetaminophen for fever. If the symptoms, worsen or persist beyond 3-4 days, it would be prudent to see her doctor.