The Mossbauer effect involves the emission and absorption of gamma rays from the excited states of a nucleus. When an excited nucleus emits a gamma ray, it must recoil in order to conserve momentum since the gamma ray photon has momentum. But this takes energy, and the gamma photon has less energy by about 1 eV for a 100 keV photon. The sharpness of an energy state in a potential target nucleus has a natural line width on the order of 10-5 eV, so that the shift in the photon energy prevents the target nucleus from absorbing the gamma photon.
Mossbauer discovered that by placing emitting and absorbing nuclei in a crystal, you could use the crystal lattice for recoil, lessening the recoil energy loss to the point that these extremely sharp emission and absorption lines would overlap so that absorption was observed. An important result was that you now had an extremely sensitive detector for energy shifts - a motion of either source or absorber with velocities on the order of millimeters per second was enough to detune the absorption.