Given that your question is asking for how sleep paralysis happens in laymen's terms, I will try to limit the technical terminology used in the answer.
All people who proceed through all four stages of sleep all are paralyzed at one point. The first three stages of sleep are categorized as NREM sleep (or Non-rapid eye movement sleep). The last stage of sleep, stage four, is called REM sleep (Rapid eye movement sleep).
It is in the fourth stage where the muscles are paralyzed. Here, REM Atonia, a time where the motor neurons are not stimulated, keep the muscles from functioning properly, if at all.
Other times, a person can become paralyzed prior to falling asleep or immediately upon waking. Paralysis prior to sleep is called hypnagogic and paralysis prior to waking is called hypnopomic.
Essentially, sleep paralysis happens because the simulations to the neurons, which make the muscles move, are not being transmitted. If the neuron is not stimulated the muscle cannot move.