Reciprocal inhibition describes the process of muscles on one side of a joint relaxing to accommodate contraction on the other side of that joint. Joints are controlled by two opposing sets of muscles, extensors and flexors, which must work in synchrony for smooth movement. When a muscle spindle is stretched and the stretch reflex is activated, the opposing muscle group must be inhibited to prevent it from working against the resulting contraction of the homonymous muscle. This inhibition is accomplished by the actions of an inhibitory interneuron in the spinal cord.
By maximally contracting the antagonist, simultaneously focusing on maximal relaxation to the agonist, I have been able to make a significant leap in range of motion, plus strengthening the antagonist by using the flexibility tension in the agonist.