A Hermitian operator is a special type of linear operator in quantum mechanics that has real eigenvalues and orthogonal eigenvectors. This means that when you measure a physical quantity represented by a Hermitian operator, the possible outcomes are real numbers, which correspond to observable values. Hermitian operators are crucial in quantum mechanics because they ensure that the probabilities calculated from their eigenstates are meaningful. They also guarantee that the system's evolution remains consistent with the principles of quantum theory, making them essential for understanding phenomena like quantum states and wave functions.