The acronym means "count per inch" and is a measure of the sensitivity of the mouse. The higher the count, the faster the cursor moves over the screen. The button allows you to change the "speed" as you are playing. Faster cursor movement means a bit less control for fine details, so great for movement around the screen. But you can go back to higher sensitivity for fine detail work.
The idea is that the mouse has its cursor speed set on the machine, (you can alter this with some software drivers), but this speed is not always the optimum for some actiivities on-screen, so you want some way of changing this quickly, without going to the mouse settings.