In general an immune response cause your white cell count to go up, and will go down if there is a deficiency, disorder or during chemotherapy.
White blood cells aka leukocytes are the cells responsible of defending the system against any disease. There are many different types of white cells, like neutrophils, lymphocytes, eosinophils, basophils and monocytes each have a different count and functions. In general the overall white cell count is between 4,000 and 11,000 per cubic millimeter.
Here is another similar question that I found on akatoo that may help:
Here is some reference I found regarding low blood cell count:
and the wikipedia link for general info on White blood cell: