Box Blur is similar to Fast Blur and Gaussian Blur, but Box Blur has the added advantage of an Iterations property, which allows you to control the quality of the blur.
So basically the basic blur adds a sort of box-ish blur to the image. However, the more iterations, the more times the blur is applied over the image. So if you have a blur radius of 10, and an iterations of 5. It will blur the image with a radius of 10, 5 times.
Blur radius is basic, nothing crazy, iterations increases the complexity of the blur. However, the render time is increased dramatically with the more iterations you add.
The highest amount of iterations you can have is 50.