A horizontal band containing decorative or narrative imagery. The term is normally used when a work of art is organized in multiple horizontal bands. On flatware like dishes these registers are often called borders that can be applied in several registers, as in border outside a border and so on. In Yongzheng period (1723-35) export porcelain one especially elaborate kind of decoration was called "seven border plates" by the Duveen brothers antiques dealers.
In describing Straits Chinese porcelain the concept of registers is especially helpful, since they seems to have loved their textile inspired 'borders upon border' decorations and those can hardly be described without referring to its various registers.
As in classical architecture any description should begin at the top and go downwards. In flat objects you describe the registers from the outside and in. In both cases you begin with the main center decoration if any.