Fiber is a rewrite that makes it easier for us to add new features to React (and it adds some). It also adds the foundation for enabling better perceived performance in the future releases thanks to async pre-rendering and more control over scheduling. That part is still work in progress and won't be enabled in React 16 by default.
So we do think eventually it’ll enable us to build more responsive apps, but we’re still working out the details and experimenting with what it can do. Don’t expect any drastic changes on this front in React 16.