While the answers here are all correct, Babel is not just about ES6 (ES2015). The ECMA standards committee has agreed to release yearly updates to the JavaScript language. Babel will always integrate the standards, whereas we don't know if all the browsers will, and if they do, whether they will be able to keep up with the changing standards.
With a transpiler like Babel, we can stay ahead of the web browsers and use new features of ECMAscript when they are released instead of waiting for the browser manufacturers to integrate the features, use polyfills, or whatever else. It also allows the end user to customize the features that they want to use and build their own version of the language.
To hear the creator of Babel talk about this, you can listen to this JavaScript Jabber episode.
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