what relation between anonymous function and delegates

Technically, an 'anonymous method' is classified as a special value which has no type but which is implicitly convertible to a compatible delegate type.

An example may make this somewhat metaphysical definition easier to grasp:

delegate int Transformer(int i);

Transformer cube = delegate(int i) { return i * i * i; };
Console.WriteLine(cube(5)); // 125

So here the anonymous method is compatible with the Transformer delegate type because it takes a single int parameter and returns an int.

Consequently, when you assign the anonymous method to the Transformer variable, cube, it's immediately converted to the Transformer delegate type.

You can then invoke the anonymous method via the delegate and cube(5) produces, as expected, 125.