nesting of class

Thank you

Nested classes are treated as static members of the containing class.

So to access the nested class B in class A, the syntax is A.B.

'b' is then declared as a variable of that type and is assigned a new object in which the variable 'a' , containing a reference to an instance of A, is passed to the constructor.

How to explain the code A.B b = new A.B(a); in the above program?

If by 'reimplement A', you mean get access to A's instance members within the nested class B, then the usual way is to pass an A reference to B's constructor. For example:

using System;

class Test
{
    static void Main()
    {
       A a = new A();
       A.B b = new A.B(a);
       Console.ReadLine();
    }
}

class A
{
    private void AMethod()
    {
       Console.WriteLine("Hello from AMethod");
    }

    internal class B
    {
       A a;
         
       internal B(A a)
       {
          this.a = a;
          BMethod();
       }

       private void BMethod()
       {
          Console.WriteLine("Hello from BMethod");
          a.AMethod();
       }         
    }
}

Notice that B even has access to A's private members.