You've created an inner class here. Since the life-time of objects of this class can potentially be much greater than the runtime of the method invocation (i.e. the object can still exist long after the method has returned), it needs to "preserve" the state of local variables that it can access.
This preserving is done by creating an (invisible, synthetic) copy inside the inner class and automatically replacing all references to the local variable with references to that copy. This could lead to strange effects when the local variable were modified after the inner class object was created.
To avoid this, there is a requirement that all local variables that you access this way are final
: this ensures that there is only ever one possible value for the local variable and no inconsistencies are observed.
This specific rule can be found in §8.1.3 Inner Classes and Enclosing Instances of the JLS:
Any local variable, formal method parameter or exception handler parameter used but not declared in an inner class must be declared final. Any local variable, used but not declared in an inner class must be definitely assigned (§16) before the body of the inner class.