You can see part 1 here and part 2.1 here
I always thought that Anonymous Methods came out with .NET framework version 3.0 
when I dig more I reliased that it came up with version 2.0.
Anonymous Method means that you can create a method - block of code - without giving it a name and execute it. The question is how can I execute it? And why do I need such a feature.
We always use Anonymous Methods with delegates although I don't like it as such. I consider Anonymous Methods is the step just before lambda methods. About the usage I only see its benifit in small programs where you try something. From my point of view I don't recommend using it as it may lead to bugs that may be hard to trace. Use it with care.
Here how can we us Anonymous Methods
1 using System;
2
3 namespace ConsoleApplication2
4 {
5 class Program
6 {
7 delegate int Square(int x);
8
9 static void Main()
10 {
11 Square square = delegate(int power)
12 {
13 return power*power;
14 };
15
16 Console.WriteLine(square(10));
17 }
18 }
19 }