A partition function is a mathematical tool used in statistical mechanics to describe the statistical properties of a system in thermodynamic equilibrium. It sums over all possible states of a system, weighing each state by its energy and temperature. This function helps in calculating important thermodynamic quantities, such as free energy, entropy, and pressure. In the context of quantum mechanics, the partition function can be expressed as a sum or integral over the energy levels of a system. It plays a crucial role in connecting microscopic properties of particles to macroscopic observables, allowing scientists to understand how systems behave at different temperatures and conditions.