Definition. A high hemoglobin count indicates an above-average concentration of the oxygen-carrying protein hemoglobin in your blood. Hemoglobin (Hg or Hgb) is the main component of red blood cells. Hemoglobin count-also referred to as hemoglobin level-indicates your blood's oxygen-carrying capacity.A high hemoglobin count is somewhat different from a high red blood cell count, because each cell may not have the same amount of hemoglobin proteins.he threshold for a high hemoglobin count is slightly different from one medical practice to another. It's generally defined as more than 17.5 grams (g) of hemoglobin per deciliter (dL) of blood for men and 15.5 g/dL for women.