Javascript Libraries
Javascript Library Reference
What is a Javascript Library? A JavaScript library is a library of pre-written JavaScript which allows for easier development of JavaScript-based applications, especially for AJAX and other web-centric technologies.
AngularJS
Layman's: AngularJS is useful for web applications for data-binding, javascript templating, multiple views, and more. Very easy to create a lightning fast live search, and multiple views in to data. Angular is more of a "Framework" than a "Library".
What their site says: HTML is great for declaring static documents, but it falters when we try to use it for declaring dynamic views in web-applications. AngularJS lets you extend HTML vocabulary for your application. The resulting environment is extraordinarily expressive, readable, and quick to develop.
Backbone
What their site says: Backbone.js gives structure to web applications by providing models with key-value binding and custom events, collections with a rich API of enumerable functions, views with declarative event handling, and connects it all to your existing API over a RESTful JSON interface.
Ember
Ember makes Handlebars templates even better, by ensuring your HTML stays up-to-date when the underlying model changes. To get started, you don't even need to write any JavaScript.
jQuery
Layman's: DOM manipulation
Mustache
Layman's: Javascript Templating
What their site says: Logic-less templates.Mustache can be used for HTML, config files, source code - anything. It works by expanding tags in a template using values provided in a hash or object. We call it "logic-less" because there are no if statements, else clauses, or for loops. Instead there are only tags. Some tags are replaced with a value, some nothing, and others a series of values. This document explains the different types of Mustache tags.