Why use the params keyword?

With params you can call your method like this:

addTwoEach(1, 2, 3, 4, 5);

Without params, you can’t.

Additionally, you can call the method with an array as a parameter in both cases:

addTwoEach(new int[] { 1, 2, 3, 4, 5 });

That is, params allows you to use a shortcut when calling the method.

Unrelated, you can drastically shorten your method:

public static int addTwoEach(params int[] args)
{
    return args.Sum() + 2 * args.Length;
}