JavaScript on the Web
On the modern web, JavaScript is a foundational element of software development. JavaScript runs in the web browser, making it a critical client-side scripting language. But implementations like Node.js allow JavaScript to run on a server allowing for server-side applications to be written in JavaScript, too.
Websites might use backends written in Python or Ruby or Java, but every website uses JavaScript. It's the most ubiquitous language online, and it is used to do virtually everything.
Application Frameworks
Building JavaScript applications like Gmail or Facebook requires a cohesive framework that will allow developers to coordinate different data, views, and functions. To accomplish this, many different JavaScript frameworks have been created.
To help get an idea of the differences between frameworks, check out the TodoMVC website, which archives versions of the same Task List application written in different technologies.
Server-Side JavaScript
With the advent of Node.js, server-side JavaScript has become more and more popular. These frameworks help you build server-side components of websites (and some of them crossover to helping with the client-side implementation, too).
JavaScript is also popular for creating some of the most hyped non-relational databases:
Game and Animation
JavaScript has replaced a lot of proprietary technologies that were used for doing game and animation programming. In the move to eliminate plugins (which are painful for both developers and users) and bring the web to a more standardized place, JavaScript has filled this niche. Here are some interesting JavaScript game and animation frameworks that are popular online today.
General Purpose
There's too much to list all of the different popular JavaScript modules and libraries used in web development today. To browse more of the popular tools available to modern web devs, take a look at JavaScripting.com. That site indexes hundreds of JavaScript modules and libraries, all sorted and searchable for your browsing convenience. The biggest problem with the JavaScript ecosystem today is that there are so many players.