What is Color Sampling?

Any time a new camera is introduced to the market, one of the key specs that gets bandied about is "color sampling." Is it 4:4:4? 4:2:2? 4:1:1?

What do all these numbers mean, and how do they relate to how our images look? Here's a simple explanation with good diagrams for comparison, written by Graeme Nattress, published courtesy of Larry Jordan and Associates.