To do something rhythmically is to do it in a repeating, almost musical way. If you’re washing a huge pile of dishes, you might notice yourself moving rhythmically as you wash, rinse, and repeat.
Music has rhythm, a repeating pattern of beats. To do something rhythmically is to do it in a way that includes or resembles the beat of music. The clanking and banging sounds of a factory might repeat rhythmically. To dance is to move rhythmically. A well-executed play in football or basketball could be performed rhythmically. This word suggests both skill and repetition.