This is not a class about how use things that you hide in your closet. (That would be a completely different word, "discreet".) This spelling, "discrete," refers to objects having distinct, separable parts, in contrast to things that are smooth, unbroken, continuous. (Such as the continuous physical space around us, or the continuous differentiable functions you dealt with in your calculus course.) And by the word "structures" in this class we refer not to physical objects, but rather conceptual mathematical structures, composed of some countable number of distinct parts.
Discrete structures are important and practical because they form the fundamental conceptual basis of all of digital information processing. Everything a computer does, it does by using discrete operations to manipulate discrete structures that are represented in its memory. The language we use to design and program computers is largely just the mathematical language of discrete mathematics.
Some amount of discrete math concepts are also used throughout all areas of mathematics, physics, engineering, and computer science, and in many areas of economics, business, industrial engineering, and operations research. Discrete math is also a useful tool for precise logical reasoning about complex but well-defined issues in just about any area.
At this point we stop to handle administrative issues, and pick a student to take notes for the first topic.
In the remaining time, we begin topic #1, Fundamentals of Logic.
At the end of class, students write their feedback, and homework assignment #1 is handed out.