  We study the spectral and orbital stability of elliptic function solutions
for the focusing modified Korteweg-de Vries (mKdV) equation and construct the
corresponding breather solutions to exhibit the stable or unstable dynamic
behavior. The elliptic function solutions of the mKdV equation and related
fundamental solutions of the Lax pair are exactly represented by theta
functions. Based on the `modified squared wavefunction' (MSW) method, we
construct all linear independent solutions of the linearized mKdV equation and
then provide a necessary and sufficient condition of the spectral stability for
elliptic function solutions with respect to subharmonic perturbations. In the
case of spectrum stability, the orbital stability of elliptic function
solutions is established in a suitable Hilbert space. Using Darboux-B\"acklund
transformation, we construct breather solutions to exhibit unstable or stable
dynamic behavior. Through analyzing the asymptotic behavior, we find that the
breather solution under the cn-type solution background is equivalent to the
elliptic function solution adding a small perturbation as $t\to\pm\infty$.
