The Vue Transition component helps animate elements when they appear or disappear. When a wrapped element is added, Vue applies CSS classes to start the enter animation, switching classes between frames to trigger CSS transitions. It waits for the animation to finish before removing the classes and showing the element fully. When the element is removed, Vue applies leave animation classes and waits for the animation to finish before removing the element from the DOM. This process ensures smooth fade or slide effects. The key variables tracked are the show boolean controlling visibility, the element's presence in the DOM, and the CSS classes applied during each animation phase.