The Woodward-Hoffmann rules are a set of principles in organic chemistry that predict the outcomes of certain chemical reactions, particularly those involving pericyclic reactions. These rules help chemists determine whether a reaction will proceed through a concerted mechanism, where bonds are formed and broken simultaneously, or through a stepwise mechanism. The rules are based on the conservation of orbital symmetry, which means that the symmetry properties of molecular orbitals must be preserved during a reaction. By analyzing the symmetry of the reactants and products, chemists can predict whether a reaction is allowed or forbidden, guiding them in designing and understanding chemical processes.