The respiratory center is a group of neurons located in the brainstem, specifically in the medulla oblongata and pons. It plays a crucial role in regulating the rate and depth of breathing by sending signals to the muscles involved in respiration. This center responds to changes in carbon dioxide, oxygen, and pH levels in the blood to maintain proper gas exchange. The respiratory center works in coordination with other systems in the body, such as the nervous system and circulatory system. It ensures that the body receives enough oxygen while removing carbon dioxide, which is vital for maintaining homeostasis and overall health.