For most people, the most important aspect of Free software (open source software) is that it is free. However, not only is it free, it can never be anything else but free. I realise that, at first glance, the whole system seems quite unusual.
There are many licenses which are considered "open source" by OpenSource.org but the one which you are most likely to hear about is the GPL ("Gnu Public License"). The idea, in its most basic form is that one can not only download the program from the site for free, you can also get a copy of the "source code".
The first analogy that springs into my head is that of a recipe. Your mother (or father, but this isn't a lesson in political correctness) may make you a stunning dessert every Christmas and give it to you for free. If you are anything like me, that situation is excellent and would be much appreciated. That dessert is like the program (or "binary") which you can get to run on your computer. In addition to that, however, you may want to make that dessert yourself or, if you are also a good chef, make some improvements to it to make a better dessert, a slightly different version of the dessert or a dessert that was less fattening. This is where the analogy becomes important. With most computer software you can only buy the cake, or get a free sample of the cake; with Free software, you have access to the recipe.
It is difficult to imagine why it would be that anyone would write something and then give it away. Each group will probably have a different reason, but some reasons could be those which follow. Some will write a program because there is nothing available that can do it. It may be that they wrote it for personal use and are more than happy to give it away to anyone who is interested in a gesture akin to charity. It may be that they write the code because it will do something that they need, but they would like to have others look over the code and help them to find bugs and add features to the code. Some do it to make a difference to the computer world.
Lately there is more of a commercial contribution to Free software. A large number of manufacturers, from those who make networking equipment to those who make cellphones, are replacing their proprietary software with Free software in order to take advantage of the huge community of programmers who are willing to contribute to making their software as efficient as possible.
There is only one condition to using Free software source code: if you change a program's source code, enhance the 'recipe', then you must make that 'recipe' just as available as the original (at least, this is the case with the majority of licenses).
An interesting side-effect of the Free software idea is that their focus is completely opposite to that of proprietary programs. Someone who is selling software for a profit has a vested interest in locking you in to only using that software for ever. Free software, however, is made by the users and aims to be as compatible as possible; using open standards in order to allow the program to talk to as many other programs as possible.
If you are interested in having a go at 'this Free software thing', I would suggest that a good starting point is to follow the link on the left hand side of this page to the Firefox website. This open source web browser has taken the world by storm and is showing people that open source software is not just a possible substitute, but a better choice. If you do not like it, it has cost you nothing and you are exactly where you began!