The quadratus lumborum is a flat, roughly square muscle deep in the side of the lower back, running from the top of the pelvis to the lowest rib and the low-back vertebrae.
It bends the trunk to the side and helps extend it. How much it stabilises the spine is debated, but it works hard in heavy lifts and side planks.
StatPearls doubts it is a significant stabiliser, noting it produces little force in sideways tilt. A fine-wire EMG study found it working at 74% of maximum in heavy barbell lifts and 54% in a side plank, more than other muscles, and called it a better spinal stabiliser than the psoas.
Trigger points in the QL can produce pain that mimics other low-back problems, and nerves running near it can be irritated. There is no agreement that a change in its tone is a primary cause of back pain.
Anatomy and movement education, not a diagnosis or treatment plan. If you have pain that follows an injury, is severe or getting worse, or comes with numbness, weakness or swelling, get it assessed. Health disclaimer.