Here's the brief answer, as I understand it: they're frameworks that provide model-view data binding, ease data/presentational decoupling, and (in some cases) provide single-page app (SPA) infrastructure in the mode of MV*. In short, they're designed to tackle some of the common complexities that arise when writing feature-rich multi-part SPAs.
You can do it all on your own, for sure, and I actually think that writing a complex front-end-heavy application without anything but jQuery is a really great way to show yourself the potential use of these libraries. It's not really super hard to write decent, well-structured and segregated code... but it does begin to feel, after a while, like you're spending your time hooking up wires you've hooked up before.
At that point, you either write your own abstraction, or you go looking for an abstraction that someone else (preferably smarter than you) will maintain.
You can do it all on your own, for sure, and I actually think that writing a complex front-end-heavy application without anything but jQuery is a really great way to show yourself the potential use of these libraries. It's not really super hard to write decent, well-structured and segregated code... but it does begin to feel, after a while, like you're spending your time hooking up wires you've hooked up before.
At that point, you either write your own abstraction, or you go looking for an abstraction that someone else (preferably smarter than you) will maintain.