Java multi-dimensional arrays are arrays of arrays, allowing the storage of data in multiple dimensions. A common example is a 2D array, which represents a matrix with rows and columns. To declare a 2D array, use syntax like int[][] array = new int[3][4];, where 3 represents the number of rows and 4 the number of columns. Multi-dimensional arrays can extend to three or more dimensions. Accessing elements requires specifying indices for each dimension, like array[2][3]. These arrays can be useful for representing grids, tables, or other structured data in a compact and organized way.