Mechanics is the study of the motion of material objects. Classical or Newtonian mechanics deals with objects and motions familiar in our everyday world. Most people possess some intuition about classical mechanics; we all have watched a ball fly through the air or a bicycle tire spin. You should not be afraid to connect the formalism with your intuition. Indeed, this is often the easiest way to see the answer to a difficult problem. Allow the formal physics and math to illuminate what you already know.
Although textbook examples usually deal with blocks, springs, and other mundane devices, keep in mind that classical mechanics describes phenomena on a vast range of scales, from large molecules such as DNA to the planets of our solar system and beyond. All of these diverse systems obey basic laws of physics.