In the 1980s, everything changed. The world became more corporate, and with the rise of the desktop PC, the concept of proprietary software became prevalent. More and more companies started to sell software. They reasoned that this was impossible to do if they shared it with everybody else, so they kept it secret. Microsoft led this charge and did very well with its proprietary software.
To Stallman, this "trade secrets" approach to software was anathema. He had nothing against software being sold for a profit, but he hated the fundamental ideas behind software being kept secret. He felt passionately that sharing software and being able to understand how it worked was akin to free speech—necessary and vital for the furthering of technology, and therefore society itself. How could the new generation of programmers improve on the previous generation's work if they were unable to see how it worked? It was absurd to need to create software from scratch each time, rather than taking something that already existed and making it better.
Because of his beliefs, Stallman resigned from his job in the MIT Artificial Intelligence Lab and founded GNU. His aim initially was to produce a complete clone of Unix that would be shared in the ways he knew from the early days of computing. This software would be available for everyone to use, to study, and to adapt. It would be free, in the same sense as free speech— shared and unrestricted. This gave rise to the vital concept of "free software" and soon GNU, and the FSF, became not just a programming venture, but also a political movement.
A very common misconception of "free software" is that it is always free of charge. This isn't correct. The word free is used here in its political sense, as in "free speech." Many companies and individuals make a healthy profit from selling free software and, in fact, selling free software is encouraged by the GNU Project.
To protect the rights of people to share and adapt the GNU software, Stallman came up with the GNU Public License (GPL). Various drafts of this license were produced over time, until it became a completely watertight legal contract, which furthered the concept of free software.
Most software you buy comes with a license agreement—that big chunk of text you must agree to when installing software (in the case of Windows desktop software, it's frequently referred to as the End-User License Agreement, or EULA). The license agreement usually says that you cannot copy the software or share it with friends. If others want to use the software, they must buy their own version.
The GPL turns this on its head. Rather than restricting what people can do with the software, it gives them permission to share the software with whomever they wish. However, if they modify the program in any way, and then distribute it to others, the program they come up with must also be licensed under the GPL. In other words, people cannot make changes to a program that has a GPL, and then sell the modified program, keeping their improvements secret.
An interesting side note is that the actual wording of the GPL says that any changes you make should be shared with others only if the software is redistributed. This means that if you modify some GPL software and don't give it to anyone else, there's no need for you to publish your changes or make others aware of those changes.