Open Source doesn't necessarily mean Free Software although it typically is. Open Source means that the source code that make up an application is available to you. As such, you can modify the code and make the application better provided you then make your new code available for others to improve as well.
Who makes open source software? there are many companies that sponsor a myriad of open source projects but ultimately, the software development is left to a worldwide community of software developers.
Answering your question as to what popular sites use open source software, well, being that Apache is the most common Web Server Software running behind the scenes, chances are you've used Open Source many times already!! A more tangible example is Yahoo! Finance using Open Source MySQL Database check out: http://www.mysql.com/news-and-events/generate-arti...
Another prime example of Open Source is Mozilla Firefox and Thunderbird.
I touch on some this on my hub:
Hope this helps !