When something happens rhythmically, it keeps a steady beat you could clap along with: a drum, a dancer’s feet, rain on a roof, a pencil tapping on a desk. The word is an adverb, so it tells you how something is done, not what the thing is. You use it for sound, speech, and movement — a speaker who talks rhythmically, a runner whose steps fall rhythmically, a baby breathing rhythmically in sleep. It does not have to be music. People stretch it to mean “again and again in a regular pattern,” even for a machine or a flashing light. It is the ordinary adverb from rhythmic / rhythmical, and it is not a fancy or rude word; you hear it in class, in sports, and in everyday talk. Though actually, in casual speech many people just say “in time” or “to the beat” instead of this longer word, and they save rhythmically for when they want to sound a little more careful or descriptive.