What is a system? What is a dynamical system? Systems are characterized by a few central notions: their state and their behavior foremost, and then some derived notions such as reachability and observability. These notions pop up in many fields, so it is important to understand them in nontechnical terms. This chapter therefore introduces what people call a narrative that aims at describing the central ideas. In the remainder of the book, the ideas presented here are made mathematically precise in concrete numerical situations. It turns out that a sharp understanding of just the notion of state suffices to develop most if not the whole mathematical machinery needed to solve the main engineering problems related to systems and their dynamics.