It is difficult to show what design is about, even if you just want to explain a few aspects of what characterizes the design process. This little video by Apple is in my mind an amazing good and rare example. In two minutes they cover the importance of first intentions, desiderata, service, composition, etc. framed in Apple language. All core concepts from our book "The Design Way".
Of course the video does not give a full exposition of design, but it presents some reflections of its core. And they do it in a beautiful way!