What does the medical abbreviation cbc w diff mean?

Complete blood count with differential. Total leukocyte count gives the total number of white blood cells per microliter of blood. The differential count gives the percentage of the various types of white blood cells like neutrophils, lymphocyts and eosinophils.
A CBC is a complete blood count.

It contains:

RBC - number of red blood cells

MCV - average volume of individual red blood cells

MCHC - average amount of hemoglobin per red blood cell

RDW - the average size of the red blood cell

Hemoglobin

Hematocrit

WBC - number of white blood cells.

If it is ordered with a differential, then they want the lab to break down the different types of white blood cells, such as neutrophils, lymphocytes, monocytes, eosinophils, as monocytes.

Different types of diseases cause a rise in the different types of WBCs, so a differential can often be useful in narrowing down a diagnosis.