Need Clarification and Explanation On This C# Code

So I have the following code from the Delegates video in the Querying with Linq course. I need some help on understanding some bits on it. The first thing that I need help with is this line:

Console.WriteLine(string.Format("Hello, {0}", name));

I understand passing in the text and the name property. However, what is the {0} for? How is that used to get the input name later in the code? The last bit I need help on is actually basic stuff, but have forgotten what it means:

SayGreeting sayGreeting = new SayGreeting(SayHello);

I know that the sayGreeting part is basically naming the method so we can use it later on. The new SayGreeting(SayHello) is saying we want to create a new SayGreeting method and pass in the SayHello method. The part I'm a little confused on is the first part. We write SayGreeting before it all, and I have forgotten what part of the code this is and why we need it. Hopefully my question makes sense, and that someone can help re-explain this to me.

using System;

namespace FunctionalProgramming
{
    class Program
    {
        delegate void SayGreeting(string name);

        public static void SayHello(string name)
        {
            Console.WriteLine(string.Format("Hello, {0}", name));
        }

        public static void SayGoodbye(string name)
        {
            Console.WriteLine(string.Format("Later, {0}", name));
        }

        static void Main(string[] args)
        {
            SayGreeting sayGreeting = new SayGreeting(SayHello);
            Console.WriteLine("What's your name?");
            string input = Console.ReadLine();
            sayGreeting(input);
           Console.ReadLine();
            sayGreeting = new SayGreeting(SayGoodbye);
            sayGreeting(input);
        }
    }
}