A torque is a "rotational force" or the rotational equivalent of a force,
torque = moment arm x force
An object in equilibrium is at rest. It is not moving (or "translating") and it is not rotating.
There are two conditions of equilibrium.
That a body is not moving (or "translating") means the sum of the forces is zero,
F = 0
That a body is not rotating means the sum of the torques is zero,
The center of mass has been called "a uniquely interesting point". The center of mass is the "average position" of the mass. You may think of any extended object as a rigid, massless shell with all of its mass concentrated at the center of mass.
Equilibrium Homework Return ToC, Rotational Dynamics (c) 2005, Doug Davis; all rights reserved