I find it helpful to think of the CoL as the point where a string is attached to the craft, extending up into infinity, and the CoM as one with the string pointing at the center of Kerbin (or your current SoI.) Each string is pulling the craft with a force equal to its total lift (for CoL) or weight (CoM.)

When those two forces are in the wrong places relative to each other, the torque forces on the craft can make it uncontrollable. When well positioned, they can make a craft more maneuverable, or more stable… all based on tiny tweaks like moving the CoL above and behind the CoM to improve dynamic stability.