Delegates are used to solve an Access issue. When ever you want to have object foo that needs to call object bar's frob method but does not access to to frob method.
Object goo does have access to both foo and bar so it can tie it together using delegates. Typically bar and goo are often the same object.
For example a Button class typically doesn't have any access to the class defines a Button_click method.
So now that we have that we can use it for a whole lot things other than just events. Asynch patterns and Linq are two examples.