Flow cytometry is a technique for detecting and quantifying the physical and chemical properties of a population of cells or particles.
It's a method for counting and analyzing cells that involves incubating them with one or more fluorescently labelled antibodies and/or other molecules that can bind to biological components, then measuring the fluorescence intensity of each Fluor for each cell.
It's used to count the amount of different types of cells, as well as the number of cells at different phases of development or the cell cycle.
A flow cytometer, on the other hand, is a device that passes a stream of cells past it and measures their fluorescence using the flow cytometry technique.