Reciprocal Inhibition is a type of neural circuit, or reflex arc, working with the brain/spinal cord and muscle relationship. It is tasked with maintaining balance between the agonist muscle and the antagonist muscle. The idea is this: when the prime mover engages or contracts, the antagonist, or opposing muscle, automatically relaxes. It really is a brilliant reflex in that it saves the organism from wasting energy as it moves.
For example, the quadriceps group and the hamstring group have an agonist/antagonist relationship. The quadriceps work to straighten the leg at the knee and the hamstrings work to bend the leg at the knee. When the quadriceps contract to straighten out the leg, the hamstrings automatically relax to allow the leg to straighten. If you are using energy to straighten your leg, it doesn’t make any sense to also use energy to bend your leg at the same time. And you don’t even have to think about it. Imagine how much energy you would waste if every time you wanted to straighten your leg, your quads had to over-power your strong hamstring muscles because they were firing at the exact same time. It would be horrible. Luckily, your body is super thrifty and uses things like reciprocal inhibition to save energy and make your body a much more efficient mover.
You can also use this information consciously to your advantage when stretching, particularly in an active-static stretch. If you are stretching the back of your thigh (to stay with that example), gently firing the quadriceps at the same time will help to further release the hamstrings. Of course, remember that being mindful, slow, and gentle is an important component in doing this safely and correctly.