Torque

I took a quick look at the Wikipedia article on torque: https://en.wikipedia.org/wiki/Torque#Units

Here's my understanding:  Torque has units of force x distance.  Think of using a wrench to turn a sticky bolt.  You need a certain amount of "twisting force" or "torque" to free the bolt.  To get enough torque to turn the bolt, you can use a short wrench and pull hard, or a long wrench pull less hard.  The torque is equal to the amount of linear force (how hard you pull on the wrench) times the length of the wrench.

According to the Wikipedia article, "12kgcm" uses "kg" to mean the weight of a 1kg object at the surface of the Earth.  "1kg" really means 9.8N, the gravitational force of the earth on a 1kg object.

Assuming this is the correct interpretation of "kgcm" units, 12kgcm means that this motor can lift a 12 kg object using a cord that's wrapped around a 1cm radius wheel.  Alternatively, it can lift a 1 kg object using a cord wrapped around a 12cm wheel.  The 1cm wheel can raise more weight, but it has to turn 12 times as fast to get the same effect as the 12cm wheel.

The Earth provides 1G of acceleration.  So a 12kg robot with 1cm wheels should be able to accelerate at 1G on a flat surface.

Anyway, this is my understanding from basic physics I haven't though about in years.  I hope people with actual battle bot experience chime in.

The torque as defined by johnbeetem is correct, I'll try to show you the concept with a couple of images. The short definition of torque in a a DC motor (always we speak of torque also in other rotating shafts mechanical applications) can be the following:

The quantitative measure of the tendency of a force to cause a rotational motion, or to bring about a change in rotational motion

Please take a look to the following image:

where R is the angle of the object to be rotated, in the unit definition a 1cm diameter wheel. F is the force that is applied to make it rotating. This applied to the specific case of a DC motor is influenced by the electromagnetic field as shown in the image below (don't matter is the scheme includes the brushes in the motor, I have not found a brushless motor design but it is the same).

Where, set E as the power supply, Eb is the electromagnetic field the motor is subject to, generating the rotation of the shaft. This express the theoretical torque, while the real value - hopefully what declared by the motor producer - consider the motor resistance to the rotation and the other electromagnetic losses. So in you case, a 12 Kg (that is as far as defined in the previous post by John as the G force on the heart) / cm is the ability of the motor to rotate a mass of 12 Kg applied on a wheel of 1 Cm radius. Based on this reference parameter, as much the wheel diameter is large, as the applied peripheral force to the wheel decreases increasing the angular speed.

Last but not least, please consider that these values are NOT CONSTANT!!!

We can expect that the producer provides a table with the torque and the other DC motor parameters ad certain conditions, like in the following for a generic motor

That should be accomplished by a curve diagram showing the DC motor efficiency response in different power conditions.

As these conditions are strongly directly influenced by the power supply respect the nominal power, this is the reason that it is better to control the motors rotational speed with PWM signal pulses instead of a voltage variations.

Enrico