It is a small miracle that the human body is so well coordinated that all of its roughly 650 muscles work in harmony to make you move. Each muscle group has an opposite muscle group that keeps it in check. When your muscles move your body in a certain way, the muscles producing the movement become the agonists. The muscles opposing the movement become the antagonists.
In a movement, like the back extension, the muscles that extend the back are the agonist. The muscles that produce the opposite movement, which is back flexion, are the abdominals. These two groups of muscles are important because they stabilize your spine. They need to have balance in order to keep your spine stable and healthy.
Back Extension Muscles
A back extension is slightly more complicated than a bicep curl because there are more muscles and more areas of the body involved. During a back extension, you contract extensor muscles of the back like the multifidus and erector spinae. These muscles run up, along the spine, from the base to the skull. They act to extend the spine, bending it backwards. In a back extension these muscles are the agonist.
On the opposite side of the body from the multifidus and erector spinae are the abdominal muscles. The most well-known ab muscle is the rectus abdominis, which is the muscle that you see when someone has a "six-pack." This muscle runs from the bottom of the ribs down into the front of the pelvis. It acts to flex the spine, which is the opposite movement of the back extensor muscles.
The rectus abdominis is not alone in its efforts to flex the spine. It also gets help from the external abdominal obliques and transversus abdominis. The external abdominal obliques are the ab muscles on the sides of your torso. These muscles run from the bottom and sides of your ribs down into your pelvis.
The transversus abdominis is the deepest ab muscle. It covers a large area, from the bottom of your sternum, down to the pelvis, and back to the sides of your hips. The rectus abdominis, external oblique, and transversus abdominis all flex the back, making them antagonists to the back extensor muscles.
Only those three abdominal muscles form the antagonist group for the back extension, leaving out the fourth abdominal muscle: the internal abdominal oblique. This muscle is sandwiched between the external abdominal oblique and transversus abdominis and is used for rotation but not flexion of the spine.
Agonist Vs. Antagonist
Having two opposing muscle groups is crucial because one can keep the other in check. In a back extension, the abdominals are keeping the lower and middle back muscles in check. If you perform a back extension as fast as possible without any weight your spine will move incredibly fast.
The job of the antagonist, the abdominals, is to slow down and stop the spine if it moves too fast or too far backward. It's important that you don't upset the balance between agonist and antagonist muscles by constantly working one side and leaving the other side alone. This can create imbalances in posture, which can lead to back problems.
It would be a disaster if both the agonist and antagonist muscles contracted at the same time. You'd freeze, unable to move! Thankfully, the nervous system has a solution for that. Reciprocal inhibition keeps the body moving smoothly by forcing the antagonist to relax when the agonist contracts.
In the back extension, when the spine starts to extend the abdominals are essentially told to relax by the nervous system. This allows the back extension muscles to lift the spine smoothly. The nervous system has the tough task of deciding when to turn the antagonist back on to stop or slow movement.