Why having a low center of mass guarantee stability?

[physics user1]

I know that, i studied it, but i can't actually make a picture in my mind, i can't really figure out why, i mean the forces and the torques are the same no? What's the big deal? What am i missing?

 

[nasu]

The torques are not the same. Imagine a rectangular prism sitting on a horizontal surface. Then incline it by some angle.
Look at the torque of the weight for two situations: low center of mass and high center of mass (for the same area of the base).
This is just part of the answer. The area of the base is also important for stability.

But no matter how low is CM there is no "guarantee". The body is just more stable, it takes a larger torque to flip it over.

 

[A.T.]

The tilt required for fall over is different.