Mechanics is the branch of physics dealing with the behavior of physical objects when they are subjected to forces or displacements. Classical Mechanics is the field of mechanics that deals the physical laws that describe the motion of bodies under the action of a system of forces at every day sizes and velocities. Together they form bases of physics.
Classical mechanics is limited in terms of the sizes and speeds at which it is applicable. The is because when the size of the objects gets extremely small quantum mechanics comes into play but on the macroscopic level quantum mechanics produces essentially the same results as classical mechanics. Further more when the speed of the objects gets extremely fast; that is approaching the speed of light relativistic mechanics comes into play while at the speed experienced in every day life relativistic mechanics produces essentially the same results as classical mechanics. Furthermore at larger scales of size and distance celestial mechanics come into play however this is actually just an expansion of the principles of classical mechanics to larger scales.
Classical Mechanics has an ancient history since the science goes back at least as far as ancient