In essence, jailbreaking your iPhone means freeing it from the limitations imposed on it by your carrier, whether that's AT&T or Verizon, and Apple. You install a software application on your computer, and then transfer it to your iPhone, where it "breaks open" the iPhone’s file system to allow you to modify it.
Why Would I Want to Jailbreak My Phone?
It lets you do everything from customizing the look of your iPhone to installing third-party applications (such as titles that are not authorized and available in the App Store) and customized ringtones on it. Depending on how far you're willing to go, you can do even more than that: Jailbreaking even lets you to unlock your phone so you can use it with a carrier other than the one from which you purchased it.
Why Wouldn't I Want to Jailbreak My iPhone?
Once you do it, you're on your own. You may have voided your warranty, so you can't rely on AT&T, Verizon, or Apple to fix any problems you encounter. All of the applications that jailbreak your phone are unauthorized and could damage or completely disable your iPhone. Your slick smartphone could end up as nothing more than a very expensive paperweight.
Oh. Why Would I Want to Do That, Again?
There's a ton of third-party apps available once you jailbreak your phone. Some of them are really fun, some of them are really useful, and plenty of them are really cool. Sure, many of them are available in the App Store, but there are many, many more unauthorized apps that are also available.
Can I Fix My iPhone if Something Goes Wrong?
Maybe. Some users have reported that they were able to connect a malfunctioning iPhone to iTunes and restore it to its original settings, which resolved the problem. Not all users have had this experience, though, and you certainly can't count on AT&T, Verizon, or Apple to provide you with tech support once you've taken this unauthorized step.