the short answer
The posterior chain is the group of muscles along the back of the body - the calves, hamstrings, glutes, spinal erectors and the lats and upper back - that extend the hips and keep you upright. Working together they straighten the hips, hold the spine tall, and pull loads toward you, which makes them the driving force behind lifting, running, jumping and standing up. Because they sit out of sight and are easy to neglect, they are also the muscles a good program deliberately trains.
This article is general training education, not medical advice. If a client has back or hip pain, this is movement coaching rather than treatment - refer out to a qualified clinician before loading a hinge.