Jailbreaking is different to iPhone unlocking. iPhones (like all mobile phones) that are sold as part of a contract are often locked to a particular network. This means that if you buy an iPhone from O2, for example, you have to use an O2 SIM card in it. The iPhone is 'locked' to that network. Unlocking the iPhone turns it from an iPhone that can only work on the O2 network to one that can work on any network. But you will still be running officially sanctioned iOS software, and still have the software limitations. (Unlocking is considered a breach of your mobile phone contract, incidentally.)
5 reasons to jailbreak your iPhone
1. It's your phone! You should be able to do what the heck you like with it
2. You can download your apps from anywhere, not just from the App Store
3. You can use alternatives to the default apps in iOS, many of which have more functionality
4. You can customise your phone's look and feel to suit your personality, rather than being stuck with the far more limited options in iOS
5. You can tether your Mac to your iPhone and bypass your networks' Mobile Hotspot feature, which is often severely restricted and/or expensive.
Jailbreaking your iPhone is relatively easy to do and (probably) legal - although the subject of Apple's official disapproval, and likely to invalidate your warranties. (You may get round this by 'unjailbreaking' your device before taking it to an Apple Store for servicing.)
The way you jailbreak your iPhone depends on which version of iOS you're running. (Brand-new versions of iOS generally cannot be jailbroken for some time after they come out. Jailbreakers will work hard to find a way to get round the new safeguards and restrictions that have been placed on the new software.) There are plenty of instructions and resources online that can help you.
Right now the easiest way to jailbreak an iPhone is to install a jailbreaking app such as Pangu on your Mac or PC. This takes admin-level control of iOS and enables it to install Cydia, the jailbreaking community's alternative to the App Store, which is packed with apps and utilities to help customise your now jailbroken phone.
Whatever you do, make sure you back up your iPhone's data before you start just in case something goes wrong.
Another reason to back up your iPhone is that you will need to be able to restore to its non-jailbroken state if you ever need to take your iPhone into an Apple Store to have it repaired. Apple Store employees will turn you away if you try to present such an iPhone to them as 1) jailbroken devices are in breach of the End User Licence Agreement (EULA) that comes with iOS; 2) and you will have effectively voided your iPhone's warranty by breaking the EULA.
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