A granulocyte is any of a class of leukocytes characterized by the presence of granules in their cytoplasm. In some medical/scientific literature, they are referred to as polymorphonuclear leukocytes (polymorphonuclear="displaying many different kinds of nucleus shapes").
These cells are active in allergic immune reactions such as arthritic inflammation and rashes. All granulocytes contain the enzyme myeloperoxidase. This class includes basophils, eosinophils and neutrophils; they are classified according to the pattern/color they exhibit when they are stained with certain dyes.
The information in this writeup was taken from the science dictionary at http://biotech.icmb.utexas.edu/; I oversaw the development of the dictionary (the website was mothballed in 1998) and I believe I wrote the entry this is based on.