Classical physics was invented by Galileo, Kepler, and Newton to deal with everyday macroscopic objects that you can see with the naked eye or with the assistance of telescopes. Classical physics—equipped with calculus and its associated equations—can describe the precise location, speed, direction, and trajectory of any visible object, from airplanes and cannonballs to stars and planets.
If you were to take a snapshot of the solar system at this moment in time, you could measure, using the equations of classical physics, the position and velocity of each planet and could predict the precise location of any one planet at any future time (within a small margin of error up to a limited but significant amount of time). The mechanics of the equations are complex, but the problems are fully soluble.
As Lee Smolin explains in his new book, Einstein’s Unfinished Revolution, this turns out to not be the case at the smallest of scales. When you start asking what matter is made of—atoms, protons, electrons, photons, quarks, etc.—a new type of physics is required, quantum physics. Quantum mechanics was invented in the early twentieth century to explain quantum physics, and seeks to describe how quantum particles behave and interact with each other.