To give a direct example from your own body: the heat is capable of beating on its own without any signals from the brain. A region of the heart called the pacemaker generates a rhythmic signal which starts a wave of muscle contraction which runs across the heart and causes it to beat in a sequence which pumps blood (random or disorganized contraction of cardiac muscle is called fibrillation, pumps little to no blood, and is what those paddles you see in ever medical show are for). The heart is only involved in sending signals which tell the pacemaker to speed up or slow down. But the basic function of the heart itself runs on its own.