ES6 brings to Javascript needed features that other programming languages already have had; like a cleaner way of writing classes, more basic collection classes, more tools for concurrency, the list goes on...
I'm no modern JS guru, but think of it as you get to advance the JS language, and use all the latest libraries independently of what version of JS is running on the client.
This is because you write in the latest JS syntax, which then gets converted into an older JS version (allowing greater client compatibility).
JQuery is still great if you only want some basic functionality - e.g. a datepicker, but if you're building Photoshop in the browser, then it quickly becomes complicated, and you'll find that you start attempting to build your own framework to support your development.
https://github.com/lukehoban/es6features