The scene — in both movies — comes following the conclusion of each film's most climactic sequence: a dance within a castle ballroom.
In "Sleeping Beauty," Prince Phillip has dispatched Maleficent (as a dragon) with a sword enchanted by those heroic fairies, Flora, Fauna, and Merriweather, and the residents of the castle have woken up to find the prince escorting Princess Aurora down the castle steps. After surprising their parents, Phillip sweeps Aurora into an effortless dance across the ballroom floor, even though no one else appears to be moving. Aurora's dress keeps changing from pink to blue, thanks to Flora and Merriweather's magical battle over her fashion.
In "Beauty and the Beast," meanwhile, the scene happens after the Beast and Belle have been reunited, Gaston has been dispatched, and the Beast has changed back into the human prince he was before the enchantress cursed him. The two get dressed up in their ballroom finery, with Belle in that iconic yellow dress, and do the exact same effortless sweep across the castle floor, in the midst of non-moving onlookers, just before the credits roll. Unlike with Aurora, Belle's dress doesn't keep changing color, so she isn't constantly surrounded by sparkles. However, reflections in the floor add a bit more depth than in the "Sleeping Beauty" version, showcasing perhaps the strides animation took in the 32 years between the two films.