"Function Types", What's the difference and why are they useful?

In the TS docs over at: https://www.typescriptlang.org/docs/handbook/functions.html, "Function Types" are introduced. The code for such an example is:

let myAdd: (x: number, y: number) => number =
    function(x: number, y: number): number { return x+y; };

Where as for the "non-typed" function it is

let myAdd = function(x: number, y: number): number { return x+y; };

To me, the extra syntax in the first example is very strange. Why is there arrow-function syntax for the return type? Why are there two parameter specifications?

Typing the function is useful if you don't know what the function will be when the variable is declared:

let myOperation: (x: number, y: number) => number;

if ( // some condition ) {
  myOperation = function (x: number, y: number): number { return x + y; };
} else {
  myOperation = function (x: number, y: number): number { return x * y; }
}

Note that in some places (e.g. interfaces) you can describe the type with or without the arrow:

interface WithoutArrow {
  operation(x: number, y: number): number;
}

interface WithArrow {
  operation: (x: number, y: number) => number;
}