It is talking about white blood cells. There are usually five kinds of white blood cells found in the blood stream. In a normal adult about three-fourths are neutrophils, about one-fourth are lymphocytes, and there will be a few of the other three (monocytes, eosinophils and basophils). Each of these cell types also have immature (precursor) forms that are common in the bone marrow, but rare in the blood stream. The “blast” you refer to is a very immature white blood cell and usually only seen in the bone marrow.
Some automated blood cell counting analyzers can determine the relative size of the cells and are only able to identify neutrophils and lymphocytes. These analyzers group everything that is not either a neutrophil or a lymphocyte into a category called “MID” meaning "mid-range" but I call it “somewhere in the middle” because these cells are between neutrophils and lymphocytes in size.
My guess is you have seen this phrase on a lab report. It is designed to let the doctors know what kinds of cells are possible in the “mid” category. Most of the time the doctors are content with this basic information. If he/she wants to know specifically what kind of cells they are, someone like myself will look at the blood through a microscope to identify them.
By the way, there are are also analyzers that can differentiate all five basic white blood cell types, eliminating the need for the "mid" category completely.