The rule of thirds comes from photography and painting and applies to interior compositions too: imagine the wall divided into three equal columns and three equal rows. Place key elements — the focal point of an arrangement, the center of a piece of art, the lampshade in a vignette — at the intersections of those lines rather than dead-center.
The reason it works is human visual perception: we read off-center compositions as more dynamic and interesting than perfectly centered ones. Centered compositions feel formal and static (which is sometimes what you want — symmetry — but often not).
For interiors, the practical applications: hanging art slightly off-center over a fireplace, placing the sofa so its back is on a thirds line rather than dead-center on the wall, photographing your room from a low corner so the focal point lands on a thirds intersection in the resulting image. This is also why AI-rendered rooms shot at thirds compositions feel more "professional" than ones shot dead-center.