There are a few schools of thought on this here are a couple (quotes pulled from various sources):
"Most people don't know the history behind the phrase "shines" which came from the nickname given to shoe shine boys who tapped in the 50s and 60s for a nickel."
"The LA style "shines" have their roots in Latin Ballroom. Couples break away from each other in the middle of a dance to start "shining". Women will extend their arms to strike a pose, then play with stylised hip and hair movements. Men’s shines tend to focus on tricky footwork based on Puerto Rican style salsa."