Fibers from each side of your cortex travel down to the spinal cord. In the brainstem they converge, then cross. In the brainstem, where the fibers converge and cross, they are visible as triangular, pyramid-like structures, hence the name. The Extra-Pyramidal System consists of cells in the basal ganglia, the cerebellum, and parts of the brainstem. These structures make-up most of the central part of the brain.
Fibers travel from the basal ganglia and cerebellum down to the spinal cord.
In the brainstem they consist of all downward traveling fibers NOT inside the pyramids, hence the name extra-pyramidal. Part of the Extra-Pyramidal System, after receiving information from the thalamus, regulates repetitive, rhythmical activity such as walking, climbing, hopping, running, rowing, and turning. The activity can be voluntary or involuntary. Thus you can be aware, or unaware, of the speed with which you're walking. A disorder of this part of the Extra-Pyramidal System, temporary or permanent, can result in involuntary, repetitive, rhythmical, regular or irregular movements such as tremor or twitching.