Is it a reference to a function?
Yes, but we generally call them methods in C#
this
refers to the current class
WelcomeUser
refers to the method name in the class.
The new MyDel
call expects to be supplied with the name of a method that takes a string argument and returns a string (i.e. something that matches the inputs and output of the delegate
). Any method that adheres to this will be acceptable

It would probably make more sense to see an example where the event raiser and consumer were in different classes:
using System;
public delegate string MyDel(string str);
class EventEmitter {
event MyDel MyEvent;
}
class EventConsumer{
private EventEmitter x = new EventEmitter();
public EventConsumer() {
x.MyEvent += new MyDel(this.MyEventHandler);
}
public string MyEventHandler(string username) {
return "Welcome " + username;
}
}
Here the EventConsumer can now know when the EventEmitter has raised its event. EventEmitter has no knowledge of any of the methods inside the consumer, what their names are etc.. The.NET runtime will call the method (in the consumer) attached to the event in the emitter. Multiple handlers can be attached:
class EventConsumer{
private EventEmitter x = new EventEmitter();
public EventConsumer() {
x.MyEvent += new MyDel(this.MyEventHandler);
x.MyEvent += new MyDel(this.MyEventHandler2);
}
public string MyEventHandler(string username) {
return "Welcome " + username;
}
public string MyEventHandler2(string username) {
return "Goodbye " + username;
}
}
They will both be called (but in what order is not guaranteed) when the event is raised..
The event mechanism is important because it allows us to provide a way to alert other classes that things have happened without needing to know anything about that class. THe obvious use is something like a Button class - Microsoft had no idea what your method that handles the button click would be called when they wrote Button, so they just provide an event called Click, and you attach any method with a compatible signature to handle the click when the user presses the button