What's the meaning of "=>" in TypeScript? (Fat Arrow)

Perhaps you are confusing type information with a function declaration. If you compile the following:

var MakePoint: () => {x: number; y: number;};

you will see that it produces:

var MakePoint;

In TypeScript, everything that comes after the : but before an = (assignment) is the type information. So your example is saying that the type of MakePoint is a function that takes 0 arguments and returns an object with two properties, x and y, both numbers. It is not assigning a function to that variable. In contrast, compiling:

var MakePoint = () => 1;

produces:

var MakePoint = function () { return 1; };

Note that in this case, the => fat arrow comes after the assignment operator.

In a type position, => defines a function type where the arguments are to the left of the => and the return type is on the right. So callback: (result: string) => any means "callback is a parameter whose type is a function. That function takes one parameter called result of type string, and the return value of the function is of type any".

For the expression-level construct, see What's the meaning of "=>" (an arrow formed from equals & greater than) in JavaScript?

var MakePoint: () => {  
    x: number; y: number;  
};

MakePoint is a variable. It's type is a function that takes no arguments and produces numbers x and y. Now does the arrow make sense?