Originally and primarily in England, Battenberg “is a light sponge cake with coloured sections held together with jam and covered in marzipan.” That’s the description according to Wikipedia. As an American, I first experienced Battenberg cake in England, although I’ve since had it State-side as well.
In a sudoku grid, Battenberg is a symbol that appears at the intersection of four cells. Wherever such a symbol appears, two of the four cells are even, and two are odd, matching the arrangement of colors in the symbol. For example, if the top left cell is a 5, then the bottom right cell is odd, while the top right and bottom left cells are even. If the top left cell were even, then the bottom right cell would be even, while the top right and bottom left cells would be odd.