The term "spinner" refers to any combat robot weapon whose main method of inflicting damage is by hitting the opponent with a spinning object.
It is critical that you understand the physics of a weapon like this in order to make it effective.
The graphic to the right and above demonstrates the concept of the "moment of inertia". Simply put, I (moment of inertia) is proportional to the product of the mass of the spinner m and the radius of the spinner R. This formula only applies to a disc, as seen, but it reinforces the main idea that:
An object requires more work to spin at a given radial rate when it has more mass that exists at a greater radius.
Terms you should know:
Impactors
Part of the weapon, typically bolted on, that is composed of a harder material than the rest of the weapon.
Asymmetric balance
The ability to find an axis around which your weapon can spin as though it were a point mass.
In this sense, the spinner is then a battery that stores energy in the form of motion. It then imparts that energy upon the other robot. By that measure, spinners are typically the most destructive / energy efficient weapons in combat robotics. That's not to say that it isn't a viable option to use these spinners' power against themselves! (consider heavyweights such as Duck, Viper Claw, or our own Slamshell)
There's a lot of math that goes into it. I plan to write this out later but, frankly, I do not have time right now. Consult http://runamok.tech/AskAaron/spinner_FAQ.html for calculators and good explanations.