What main important informations does a CBC blood count test tells a physician about a patient?

Many things. Complete blood cell count provides information about the state of red cells, white blood cells, platelets and by inference about the health status of the patient. Briefly, it provides information about anemia, infection or susceptibility to infection, bleeding tendency, blood cancers, chronic inflammation, blood loss, alcohol abuse, lead poisoning, autoimmune disorders etc.
Wbc, rbc, plt. A standard complete blood count measures red blood cells and their characteristics, platelets, and white blood cells and their types. If a peripheral smear is done (microscope), bacteria in the blood can be seen but not always identified; growing the bacteria in culture dishes identifies them.
Too much to mention. Russell, the CBC is one of the most important tests that a patient can have done. It monitors the WBC count to look for everything from inflammation to leukemia, the RBC count to see if you are anemic and the platelet count to see if this part of the clotting system is working properly.