You can consider the self-invocation function as kind of higher order function, that returns some another function with some configuration.
Okay, what that self-invocation function is doing? It does contain one constructor functions which hold one public property with name "greeting". Input parameter received from constructor function, get assigned to the greeting. After this signature, it's adding some helper function to this constructor function, with the help of prototype, which prints greeting message.
what does it mean by prototype? it's the one of the major pillar of javascript https://developer.mozilla.org/en-US/docs/Web/JavaScript/Reference/Global_Objects/Object/prototype
Well! do we really need a self-invocation function for this? the answer is, nope! we can have this written in a simple way too, just like below,
function Greeter(message) {
    this.greeting = message;
}
Greeter.prototype.greet = function () {
    return "Hello, " + this.greeting;
}; 
var greeter;
greeter = new Greeter("world");
console.log(greeter.greet());
That's it! And it will give the exact result as above.
Then why that guy used the self-invocation function for it? I believe, cool design pattern always shines. That guy has a plan to write some factory function kind of thing which would give me a fully configured constructor function. In this case, the self-invocation expression is nothing but the so called factory.
Note: in the original post by you, the outer most Greeter is not a real function, that is a simple variable which holds some function, returned by that self invocation block. You can use any name for that variable.