Unlock, Expand, Create
Jailbreaking your iPhone, it sounds caustic, problematic, and difficult, but nothing could be further from the truth. Thanks to enormous advances by a group that calls themselves the "Dev team", jailbreaking your iPhone is a fun experience that anyone with two hands and a little patience can do.
The question becomes then, "why jailbreak my iPhone"? Surely your iPhone in its current state operates just fine, makes calls, plays some games, can download apps, music, etc. What else is there to do with the iPhone that's not built in? To answer these questions let's talk about what jailbreaking a phone actually does, and how it's different from "unlocking" it.
Jailbreak is a modern term for the exploitation of flaws in the iPhone's system in order to fully unlock the potential behind the device. To put it layman's terms, a jailbreak just makes your iPhone "all that it can be" in the best of senses - allowing it to run some great apps.
The reasons behind jailbreaking your phone are numerous. Perhaps you're attracted to being able to run the greatest apps that aren't available on the iTunes App Store - including those that change the phone's background (not the lock screen, but the actual background), those that change the entire UI including icons, backgrounds, noises, etc, or even those apps that give you customized ringtones. Maybe you're drawn to the fact that you can run some great free games on there once the jailbreak is complete - including Quake for iPhone - a port of the original Quake made entirely to run on the iPhone.
Or, maybe jailbreaking is the only way that you can run the iPhone on your cellular network of choice. Keep in mind that jailbreaking the phone won't automatically unlock it (unless you select that option), and you'll still need to change out the iPhone's SIM card, a task easier said than done.
I know personally, the appeal to me was being able to run apps that I couldn't get on the app store, or change my backgrounds to a Gears of War 2 theme for a month, or even using OpenSSH to transfer files over my Wi-Fi network directly onto the phone without worrying about those pesky USB cables.