They are telling the compiler that an array is to be used.
If you have int[] matrix = new int[5]; then you're creating
an array of integers with 5 elements. The first int[] set of
brackets says hey I'm an array but I'm not telling you how
big I am. The second set of brackets  in new int[5] says
we want a new object an array of integers that will be 5
integers long. I hope this has helped a little bit.