Inner classes are classes that are defined within another class. 
● Member inner classes: These classes are defined within another class and have access to the instance variables and methods of the enclosing class. 
● Local inner classes: These classes are defined within a method and have access to the final variables of the enclosing method. 
● Anonymous inner classes: These classes are defined without a name and are typically used to provide a single-method implementation. 

Let us look into the example of these three: 

Member Inner Class

class MyOuterClass { 
private int x; 
class MyInnerClass { 
public void printX() { 
System.out.println(x); 
} 
} 
} 

This example defines an inner class called MyInnerClass within the MyOuterClass. The MyInnerClass has access to the private variable x of the MyOuterClass. 

Local Inner Class:

class MyOuterClass { 
public void printSquare(final int x) { 
class Square { 
public void print() { 
System.out.println(x*x); 
} 
} 
Square s = new Square(); 
s.print(); 
} 
} 

This example defines a local inner class called Square within the printSquare method of the MyOuterClass. The Square class has access to the final variable x of the printSquare method. 

Anonymous Inner Class: 

class MyOuterClass { 
public void performAction(final int x) { 
new Action() { 
public void execute() { 
System.out.println(x*x); 
} 
}.execute(); 
} 
interface Action { 
public void execute(); 
} 
} 

This example defines an anonymous inner class that implements the Action interface within the performAction method of the MyOuterClass. The anonymous inner class has access to the final variable x of the performAction method. 
Inner classes are often used to encapsulate functionality within a class or to provide additional functionality to a class. They can also be useful when working with events, as they can be used to define event handlers.