Jailbreak your iPhone means you are allowed to install 3rd party applications on iPhone.
Jailbreak does offer quite a number of benefits
1) Install 3rd party applications via Cydia and Installer Some of the great applications you can find on Cydia are:
Cycorder / Video Recorder – Let you capture video on iPhone
NemusSync – Sync iPhone calendar with Google Calendar
MxTube – Download and save YouTube video on iPhone
iAcces – Let you use all kinds of Chinese Input Method
iPhoneModem – Let you use iPhone as modem and give your laptop connection to Internet via iPhone
Mame4iPhone – Play arcade game on iPhone
2) Video Recording
Compared iPhone with any other mobile phone in the market, there is one area iPhone would definitely lose – Video Recording. With jailbreak iPhone, however, you can easily turn the iPhone camera into video camera for video recording by using Cycorder or iPhone Video Recorder.
3) Changing iPhone Looks & Feel
Are you bored with the standard icons that come with iPhone? Ever think of changing the look of iPhone? With jailbreak iPhone, you can use Winterboard to apply theme on iPhone and make it look even cooler. Here are just a few samples to show what Winterboard can do for you
4) Full control of your iPhone
This may not be the reason for non-tech iPhone user. But for geeks, this may be why you need to jailbreak the iPhone. As you may know, the inner part of iPhone is a trim-down version of Mac OS X, which is actually a Unix core. So, you may wonder whether you can install some Unix applications such as Apache web server, on the iPhone. The answer is yes. With iPhone jailbreak, you can install a lightweight version of HTTP server and other similiar servers. And, one server that most Jailbreak iPhone users are using is a SSH daemon. With SSH, you can connect to iPhone remotely and transfer any file to/from it. Pretty cool, right? You can further refer to this post about how you can use SSH to transfer ringtone to the iPhone.
5) Unlock iPhone Lastly, the most common reason for jailbreaking iPhone is for unlock. This is one of the mandatory steps you need to through before you can unlock iPhone. Unlocking means breaking free from your current carrier.

The benefits of unlocking your Iphone are clear: you will be able to use cheap local (pay as you go) simcards in the phone, and make phone calls at cheaper local rates. ( instead of using the expensive roaming services) You can use the iPhone on cheaper networks ( especially data rates are often very expensive on the standard iPhone carriers) You can use more then one phone number on the iPhone, and switch your simcard at any time you wish.
Of course you can always use the original AT&T ( or O2) simcard after unlocking. The unlock does not affect the way your iPhone works ( if you use a good unlocking service) it only enables the phone to accept any simcard.
Other benefits of unlocking your iPhone are the addition of Cydia and installer on the unlocked iPhone.
The benefits of unlocking your phone are numerous. Not only will you benefit from being able to use any SIM card on any network in your phone, but you will also be able to take advantage of roaming services offered by most major networks.
Unlocking your handset may also enable dual, tri or even quad band functionality, allowing you to use your phone in even more countries around the globe.