When attempting to execute a movement, a signal is not only sent from the motor cortex through the spinal chord and to the muscles, but also one is sent from the same motor cortex to the cerebellum, containing the information of what is the intended movement (this happens via the cortico-pontocerebellar tract, and enters the cerebellum through the middle cerebellar peduncle, in case you are familiar with some neuroanatomy).
At the same time, the cerebellum is receiving information about the current position and forces of the body, called proprioception, through signals that come from proprioceptors located on bones, muscles and joints, which travel up the spinal chord (through the spinocerebellar pathways) and enter the cerebellum (through the inferior cerebellar peduncle). The cerebellum then processes both pieces information - intended movement and current mechanical state of the body - and sends out a signal back to the motor cortex (via the superior cerebellar peduncle) containing information that will improve the overall execution of the movement, by correcting and smoothing out with how much force, how much time and to what extent each component of the movement should be done.
The cerebellum is also implied in the learning process, not only movement-wise (learning to ride a bike or swim), but also cognitively.
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