That's called an "anonymous inner class."
Anonymous inner classes are classes which are created within another class but not named. They are instantiated by their interface or abstract base class definition and given their missing implementation inline with the instantiation.
In this case, MenuItem is abstract - it's missing its run() method. You're providing the implementation of its run() method here on lines 2-4.
Take a look at this JavaWorld article for more information about the various types and uses of inner classes.
As for the second part of your question "what is the difference between instantiating objects inside method definitions and in "instance variable section" like this?" -- the difference is scope, and when the object is instantiated.
Non-static member variables with initial values are created when the object which contains them is instantiated. The initial value assignment (initialization) executes at that time as well.
Static member variables with initial values are created and initialized when the class is loaded by the VM's class loader. With eager ClassLoading, this will occur at the start of the application. With lazy ClassLoading, this will occur the first time the class is referenced by the application. I believe by default most classes that aren't part of the Java runtime are loaded lazily.
Both static and non-static member variables have object-level scope and are accessible by other objects according to their access modifier (public/private/protected).
Non-static member variables are part of an object instance, and as such they are marked for garbage collection when that instance is orphaned or goes out of scope. Static member variables are only garbage collected if the class that contains them is unloaded. This only occurs if the ClassLoader instance which loaded said class is garbage collected. See this question for more info about that.
Local variables (variables which are defined within a method) with initial values are created and initialized when that line is executed as part of normal method execution. They are marked for garbage collection (destroyed) once they go out of scope (after the method in which they're contained finishes executing).