The cerebral penduncle (correctly spelled cerebral "peduncle") is made of nerve fibers, and there is one on each side of the brain. They help transport nerve impulses from the higher part of the brain (cortex) and the brain stem, or lower part of the brain. The main function of the cerebral peduncle impulses is to control body movement. When there is an injury to cerebral peduncles, the symptoms of the injury show up in another part of the body that is affected by the particular part of the peduncle that corresponds to that body part.
The term "cerebral" means it is related to the brain. "Peduncle" means a stem type of structure that joins two organs. The cerebral peduncles are connected to the pons, which is a part of the frontal brain stem that looks like a swelling. Many other nerve bundles also connect to the pons.
The cerebral penduncle (correctly: peduncle) helps sharpen our movements. If body movement impulses came straight from the cortex, the movements would seem erratic and clumsy. The peduncles adjust the commands by taking into account where the body parts currently are located before causing the movement, and they sometimes slow down the movement.