One of the most popular complaints about Apple's iOS operating system is that it forces the user to exist in a "walled garden."
The user has plenty of access to apps and services, but only if those apps and services meet Apple's guidelines.
The iPhone is such a unique platform that some people find it a total shame to be forced to use Apple-approved software.
Thankfully there's another way.
Jailbreaking your phone frees it from Apple's clutches, enabling you to install and run any software you like. A jailbroken phone can do a number of new things that would never be possible with an ordinary phone.
The political "do it because it frees you" reason
Some people take offense at the fact that Apple retains control over your phone after you buy it. It's just a phone, and you own it. Shouldn't you be able to do anything you want with it?
Access to the Cydia app store
A number of independent developers contribute software to Cydia, the special app store for jailbroken iPhones.
Because these phones can run whatever software the user wants, an impressive number of new capabilities can be bestowed upon a phone (as you'll see).