I really like open source software. I think the quality of most popular open source software is pretty good, and on average it is at least on par with the quality of closed source software. At the extremes, there are open and closed projects that are unmatched; for every Photoshop and Skype there is an openssh and apache. This short blurb is about why open source software matters to you: my mother, my steel-working friend from high school, my friend from university, the intergalactic electric rodent. As various large organizations continue to lobby to remove all of our "digital" freedoms, a few reasons why open source software (and the freedom of data in general) are important to even non-technical people, and decided to write some of them down.
Available source code is useful even if you don't feel like compiling the code yourself, looking at the code, acknowledging that the code is available, or even know what code is. Think of code like a published paper in a scientific journal: it is important to not only have peer review (to spot potential errors in experiment), but also to disseminate scientific knowledge to the community on certain truths of general interest. In computing, code is the definitive document that describes the process by which a program achieves the desired result via it's inputs (your mouse clicks, your typing). Making it available to the community (of programmers) not only opens it to scrutiny, but more importantly makes the 'experiment' of that program repeatable, and lets other people continue where the original experimenter left off.
Admittedly, this is an imperfect analogy. Some people look at a program solely as functionality they have created that did not previously exist, and I'll admit that this is one of the main attractions to programming. But to the average joe, this side of software should be relatively unimportant. Software drives how you.. well, how you drive, who you vote for, what type of entertainment and information you receive. It's important that software (and also the data formats that they use) is available for scrutiny and for record so that in the future the culture we are creating and sharing, the knowledge that we are codifying, is not lost.
People don't think about that last part often; but for thousands of years our culture was preserved in cave paintings and terracotta jars. For hundreds of years, we've been using items of less permanence (paintings, books, etc), and recently we've shifted in overdrive to using magnetic and optical media; just like we can't allow pens or paper that do not allow criticism of the government, we can't allow the companies that come up with that media to dictate how we can access it and what we can put on it.
Today, we buy into systems that restrict what we can do via sophisticated (and unsophisticated) software schemes at an alarming rate. We buy DVDs that have copy protection to prevent the uneducated consumer from making a copy to play on his iPod, we purchase digital music that require the player to call home to play or restrict the number of devices we can listen to it on, we buy cell phones that have their features artificially removed in the firmware in order to provide "convenience" services like downloadable ringtones (for a price) and multimedia content (for a price).