I just start to learn TypeScript, and I saw there is a lot of code using this sytax =>. I did some research by reading the Specification of TypeScript Versio
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?
It is called a "fat arrow". It was added in EcmaScript6 and replaces the function keyword among other things.
More can be read here.