When the first Firefox browser was released, it got a lot of attention very fast. It was obvious that open sourcing the existing code was definitely the right choice. There is also a great documentary available on YouTube, called "Project Code Rush - The Beginnings of Netscape". The documentary basically tells the story about the days when Firefox was about to be released. Changing the code to make it OSS is nothing outdated - its the same thing Microsoft does these days. It actually takes a lot of time and efforts to make an existing code base a representable, functional open-source code.
Firefox did not only represent a great alternative to the stagnant IE, which was not moving the web forward, but also a great software in general. Add-ons allowed to make the browser a lot more useful (and kept the general software very lightweight), free collaborators or volunteers could identify weak points in the very good readable code base and Mozilla provided a website with technical information that was a great resource. It seems that Firefox really saved the web, leading to revolutions such as HTML5 as a technology or Google Chrome as a piece of software, which was based on a similar project called Webkit (forked from KDE). Chrome with its v8 engine is the reason JavaScript became popular.
One might ask what is still to do? Actually a lot. Let's consider the mobile phone market for a second. There are a few really strong operating systems. We have iOS (closed, very popular, but also limited to just a single vendor) and Android (open, even more popular, but exists in many flavors distributed by many vendors). We also have minor players such as Windows Phone (closed, but uniform and with many vendors) and Blackberry (same as for iOS). Every OS has their own UI framework (of course!), and requires their own programming language (at least out-of-the-box). This is a lot of commitment for a single platform.
This is actually where HTML5 / CSS3 comes to rescue. We already have a proper UI framework. With JavaScript we also have a more than capable language for such apps. It should be no surprise that such solutions are already quite popular for writing x-plat apps. Nevertheless, why not start a platform directly with such apps as first-class citizens? Mozilla thought about this and created "Firefox OS", which brings the renderer to the kernel, resulting in a nice performance boost. Additionally the JavaScript API has been greatly upgraded and Mozilla also provides a store implementation that follows the same spirit by being completely standardized and open.
Such an OS also requires more research to optimize performance. Therefore Mozilla not only created a great project called "Servo", which is a next generation browser engine, but also a new programming language called "Rust". Rust is just awesome. It basically tries to be a possible successor to C++, which drops a lot of legacy features and focuses on reliability. The language also comes with a way of distributing packages, referencing them or managing them.
Finally Mozilla is also investing heavily in JavaScript. They created asm.js, which is a subset of JavaScript, which can be compiled to very fast code, almost executing at the speed of optimized C code. Other companies such as Microsoft will also include asm.js into their engines, which enables developers to distribute their native applications as a web application. But Mozilla also created LLJS, which is the low-level JavaScript compiler. It basically serves the same purpose as LLVM, which is a machine language compiler. Like LLVM, it comes with its own language. However, unlike LLVM, which is compiling to machine dependent assembly code, LLJS compiles to JavaScript. It is therefore a great target for writing a transpiler.
I did not mention projects such as Emscripten (which is using LVVM), Shumway or broadway.js. Nevertheless, I guess the few paragraphs above indicate that Mozilla is doing a lot for advancing the web. This is an ongoing revolution and we already see parts of it being used in other great projects or products.
Hence I want to conclude with a big thank you to the Mozilla Foundation. You're doing great work!