To spank is to hit someone with an open palm, especially as punishment. You should never spank your dog, even when she chews your favorite shoes; a firm "No!" is a strong enough correction.
To spank is to slap, most often on the rear end. In some places, it's perfectly acceptable for a parent to spank their child for misbehaving, but spanking is increasingly seen as potentially harmful—and in some countries, it's even illegal. Spank is an imitative word, which means it was coined as an imitation of the sound of a spank on skin.