In Caribbean dancing, to "wine" is to gyrate the mid-section of body, specifically the waist and hips (pelvis).
The word "wining" is broken English for the word "winding", as in "a long and winding road". Winding describes something that is coiling, circling, rotating, or snaking.
"Wine" is not to be confused with the word "whine" which means to complain or to make a whining sound.
Come on, dance! Move your hips! Wine your waist!