The Dirac equation describes free propagation of the spin $1/2$ particles. It has the form Here $\psi$ is a spinor, describing the wave-function of a fermion with the mass $m$, $\gamma ^\mu$ are gamma-matrices.
The Dirac equation is analogous to the Klein-Gordon equation for the scalar particles. Moreover, the property of gamma-matrices $\{\gamma ^\mu ,\gamma ^\nu \} = 2 \eta ^{\mu \nu }$ implies that the Dirac equation square is a Klein-Gordon (or wave) equation