Jailbreaking is the term used specifically for Apple's iOS products (iPhone, iPod Touch, and iPad) that's essentially a synonym for unlocking. Jailbreaking an iPhone isn't just a nerd trick; it allows you to do all kinds of stuff Apple doesn't like, including full multitasking, running unapproved third-party apps (including those porn apps Steve Jobs hates so much), and even tweaking key features of the iOS device to your liking.
Jailbreaking is also incredibly easy, much easier than Android's equivalent, "rooting." Rooting an up-to-date Motorola Droid, for example, requires downgrading your firmware to a previous version, which can irrevocably break your phone. Then you have to load an alternate firmware onto the Droid, which can also irrevocably break your phone. The whole process is very messy and intimidating, not to mention risky. But that's not a problem with iOS.
Jailbreaking doesn't even require any downloading anymore--it used to be a one-click process, but I suppose even that was too tricky. Now you can just visit this site from your iPhone's browser, follow the on-screen instructions, and be jailbroken in no time. And if you've got an iPhone 4, there's a great reason to do just that: 3G FaceTime support.
When FaceTime was announced, we all wondered if AT&T would let Apple (further) destroy their network by allowing the data-heavy service to be used over 3G. It was no surprise when FaceTime was limited to Wi-Fi, though still disappointing. But now, you can jaunt over to this page with your newly jailbroken iPhone 4, download the My3G app, and enjoy video chat wherever you are. It's pretty amazing.
Of course, if you're on a tiered AT&T data plan, watch out, because this is, as expected, very hard on data. 9to5Mac figured out that 3G FaceTime uses about 3MB per minute--so if you're on the lower 200MB plan, you might want to rethink that hour-long video chat.