Cask Conditioning is the process of the secondary fermentation the ale undergoes before it reaches your glass. Since we generally have both the cask conditioned ale and its more familiar Yankee version, you can try them side by side to fully appreciate the difference.
Some people think the difference is quite subtle.
Others find it very pronounced. Here's a brief explanation to help you understand the differences. The cask is then set aside for a while to complete the secondary fermentation. Then the brewer preps the cask for dispensing. He broaches the cask with a tap and hammer, venting any excess pressure.