In answer to the question “What is Windows Azure?”, most explanations seem to trot out this layer diagram:
…but I find the explanation in this video produced by some of my developer evangelist counterparts in the UK to be far more satisfying. Note that this video was produced before Azure was announced to the public; in the video, the evangelists refer to Azure by its codename, “Red Dog”. Just think “Azure” every time you hear them say “Red Dog”.