Arrays in Java allow for the storage of multiple values of the same data type. An array is declared by specifying the data type followed by square brackets, and memory is allocated using the new keyword followed by the data type and size of the array. Arrays have a length property that can be accessed using the length() method. Elements in an array are accessed using indexes that go from 0 to length-1. Two dimensional arrays can also be created to store elements in a tabular format with multiple rows and columns.