The Lagrangian is a mathematical function used in physics to describe the dynamics of a system. It is defined as the difference between the kinetic energy and potential energy of a system, represented as L = T - V. This formulation helps in deriving the equations of motion for a system using the principle of least action. In classical mechanics, the Lagrangian approach simplifies complex problems, especially in systems with multiple degrees of freedom. It is a key concept in analytical mechanics and is widely used in fields such as quantum mechanics and general relativity to analyze motion and forces.