Why int[] a = new int[1] instead of just int a?

int a

defines a primitive int.

int[] a = new int[1];

defines an array that has space to hold 1 int.

They are two very different things. The primitive has no methods/properites on it, but an array has properties on it (length), and methods (specifically its on clone method, and all the methods of Object).

Arrays are a bit of a weird beast. They are defined in the JLS.

In practice, it would make sense to do this when you need to interact with an API that takes an array and operates on the results. It is perfectly valid to pass in a reference to an array with 0, 1, or n properties. There are probably other valid reasons to define an array with 1 element.

I can't think of any use cases where you would want to define an array with one element, just to bypass the array and get the element.

One is on the stack, one is on the heap.

One difference is that you can write a method that changes its int argument by changing arg[0]. This trick is used quite a bit in some of the code I've seen. It allows you to, for instance, return a boolean indicate success or failure and an int value that serves some other purpose. Without that trick, you'd have to return some sort of object containing the two values.