Classical mechanics describes the motion of particles and extended objects in response to applied forces. It is used to understand the behaviour of systems as small as bacteria and as large as the orbits of planets around stars. Classical mechanics has a long history and is the bedrock upon which many other theories of the physical world, such as quantum mechanics, build.
Quantum mechanics describes systems at the molecular scale and below, where classical mechanics' assumption of rigid particles breaks down. It can explain the macroscopic behaviour of solids and the chemical elements as a consequence of interactions on the quantum scale. Many technologies rely on quantum mechanics: solar cells, lasers, magnetic resonance imaging scans (MRI) and quantum computing to name a few.