c# code description need help

You might understand this better by the following

name => name is the same as f(name) = name, just that you do not need to include a function name (in this care the function name is f)

Therefore the first ordering.GroupBy(name => name) is saying that you want the grouping to be according the the name. Now this code creates a key that in this case only has the name and a collection of records (objects) that have the same name.

What is happening in the second part is that you are counting the records under each record which is a collection of original records that have the same key, or in this case are the same string. As a function this would be f(keyCollection) = keyCollection.Count().

This might help:

Define a class:

public class t
{
    public string Shortname { get; set; }
    public string Longname { get; set; }
}

Then put this in a console program:

var testclass = new t[] {new t {Shortname = "US", Longname = "Long US 1"},
    new t {Shortname = "US", Longname = "Long US 2"},
    new t {Shortname = "UK", Longname = "Long UK 1"},};

var testLinq = testclass.GroupBy(i => i.Shortname);

foreach (var g in testLinq)
{
    Console.WriteLine("Key = " + g.Key);
    Console.WriteLine("  Records");
    foreach (var r in g)
        Console.WriteLine("   " + r.Longname);
    Console.WriteLine();
}

Console.ReadLine();

You will get the following:

Key = US
  Records
   Long US 1
   Long US 2

Key = UK
  Records
   Long UK 1