The Slater determinant is a mathematical construct used in quantum mechanics to ensure that the wave function of a multi-electron system is antisymmetric with respect to the exchange of any two electrons, thereby obeying the Pauli exclusion principle. It is crucial for accurately describing the electronic structure of atoms and molecules in quantum chemistry, providing a foundation for more advanced computational methods such as Hartree-Fock and post-Hartree-Fock methods.