Classical Mechanics is the physics of dealing with motion of matter on a large scale (many orders of magnitude larger than the scale of atoms). The motion may be of a linear type, oscillatory type, rotational, rolling, circular and similar other types of motion encountered in nature. It is an approximation for the laws of nature and gives good results on the macroscopic scale. It was, in fact, considered to be true for matter on every scale till the 19th century. But, in the 20th century, a new set of laws and mechanics (quantum physics) was developed for matter at the atomic scale.
Classical mechanics has ideas of particles, their positions, momentum, energy and motion in space and time. Classical mechanics claims to predict the exact position, velocity, energy, momentum and other such properties of a system at any given point of time if its initial state and the forces acting on it are known. Although, it turns out that all such predictions are not possible in nature for a system to any level of accuracy (Heisenberg's Uncertainity Principle) because of the flaws in the idea of particles inherent to classical mechanics, classical mechanics still gives excellent approximations for most of our analysis of systems where such effects can be neglected.
For example, in dealing with the motion of machine parts in industry, motion of rockets in space, motion of blocks and balls on inclined planes, pullies, motion of planets around the sun and other such macroscopic systems, classical mechanics is quite efficient.
There are different approaches to the study of classical mechanics. Newtonian mechanics, Lagrangian mechanics and Hamiltonian mechanics. They are equivalent in that they lead to the same results, but provide different routes and theorems for analyzing motion.
Classical Mechanics is one of the branches of physics which is rather interesting because of its closeness to our daily experiences. Many of the mechanical phenomena we see around ourselves can be analyzed and understood on the basis of laws of classical mechanics. Easy models and mind pictures can be drawn for solving the problems. Not that the problems are less challenging, but we can relate them to our everyday experience.
( unlike, for example, quantum physics and theory of relativity).