Final answer:
The cerebellum, situated below the occipital lobe and termed the 'little brain', is critical for balance, posture, and coordinated muscle movements.
Step-by-step explanation:
The brain structure located inferior to the occipital lobe that is responsible for balance, posture, and muscle coordination is the cerebellum. This portion of the brain sits atop the brainstem and is sometimes referred to as the "little brain" due to its appearance and size in comparison to the larger cerebrum. The cerebellum plays a crucial role in coordinating movement and is also involved in learning new motor tasks. It receives messages from muscles, tendons, and joints as well as structures in our ear to help maintain balance and smooth, coordinated body movements. Additionally, it's an important area for processing procedural memory, which is essential for performing tasks that have been learned through repetition.