The Poisson bracket is a mathematical operator used in classical mechanics to describe the time evolution of dynamical systems. It is defined for two functions, typically representing physical quantities like position and momentum, and is denoted as \f, g\. The Poisson bracket helps determine how one quantity changes in relation to another, providing insights into the system's behavior. In Hamiltonian mechanics, the Poisson bracket plays a crucial role in formulating the equations of motion. It is closely related to the concept of symplectic geometry and is essential for understanding the structure of phase space, where the state of a system is represented by its coordinates and momenta.