How do Adwords auctions work?

One of the discussions I find myself having with new and old clients, involves the auction system in Adwords. Its an intricate mechanism involving the advertiser, the user and Google. Concepts like Quality Score, Relevancy and the importance of Landing Pages can be difficult to explain.

Luckily the Adwords team have just released a fantastic video tackling these very topics:

Thanks to @avinashkaushik for the tip off!