Caption: A rigid object supported by a free pivot ABOVE its center of mass will be stably balanced: i.e., in stable equilibrium.

Everyday life experience tells you this even if you don't know the expression center of mass.

For example, hanging pictures.

Some objects, like the balancing bird in the image, have unusual mass distributions, and so their centers of mass are NOT where you would guess. For balancing bird, the center of mass is under the beak which allows the balancing bird, to balance stably like a hanging object. Of course, the balancing bird is in a rather weak stable equilibrium: it does NOT take too big push to tip it. See the video Balancing Bird | 0:28.

Credit/Permission: © APN MJM, 2012 / Creative Commons CC BY-SA 3.0.
Image link: Wikipedia: File:Bird toy showing center of gravity.jpg.
Local file: local link: center_of_mass_balancing_bird.html.
File: Mechanics file: center_of_mass_balancing_bird.html.