Tutorial 95 - Line of Gravity
The line of gravity is the middle or average point of the weight distribution. If standing upright, it runs from the tip of your head through the middle of your body and to your feet. You can feel your center point shift across the sole of your feet, your support base, if you stand and lean forwards or backwards. 

If the center of gravity shifts outside of the support base then the structure (or character) will fall. This is what happens during a walk cycle. Every time a leg is thrown forward to take a step we are falling a little and then stopping the fall when the leg lands on the floor. 

For character designers, we need to be sure the weight is evenly distributed around the line of gravity. If the character pose is not symmetrical then the masses will be stacked in a way that transfers the line of support, balancing weight thoughout.