What that refers to is the trick of transforming "int a;" to "final int[] a = {0}" and then referring to a[0] everywhere. This adds about 20 bytes of overhead on Sun's 32-bit JVM and memory pressure for almost no benefit whatsoever.
final int a = 0;
is all you need in the example you provide.
For instance you may want "a" to be mutable, but you also want to use its value when the closure gets executed.
I don't think I've ever used a framework in Java that relies on event-handlers / callbacks where I didn't had to box local variables.