JQuery is one of my most favourite frameworks for JavaScript. It is lightweight, yet packs a punch! The amount of added functionality combined with the ease-of-use, makes it probably the most widely used JavaScript framework. You can read all about it here!
A useful (and free) introductory tutorial for jQuery is located here.
This is an important slide. If you want to use JQuery, and many other external frameworks or libraries on your site, you would have to embed them within your site. This is done here however you might ask yourself, where exactly are you getting this from? Well that is an excellent question! These frameworks are being hosted on CDN's ,or Content Delivery Networks, in which they allow you to use. It's actually pretty neat however you can also download JQuery for example and just host it locally. The choice is yours.
Just a quick note. JQuery is extremely good at animating elements. That is to say it provides many methods to allow for animation on your site.