Briefly, jailbreaking the iPhone means that you are allowed to install on it more than Apple applications, and these would be third party apps. This applies to all firmware versions, and it is different of unlocking the phone, which means to accept all carriers. An unlocked iPhone will accept all SIM cards from all carriers. You won't be anymore tied to one carrier, which must be approved by Apple. With the introduction of Apple store, a question appears:"Why do we still need to jailbreak the iPhone?". There are som reasons for which users want to jailbreak the smartphone, and I tried to summarize them here in this article.
Even if Apple introduced the App Store in iPhone 2.0, and even if this is the best feature for that firmware update, there are some applications developed by other companies which would be great for iPhone too. Some interesting utilities, like Netshare, NemusSync ( sync the iPhone calendar with your Google Calendar), iAccess(allows you to use all the Chinese Input Methods), or Mame4iPhone which allows you to play arcade games on iPhone, are developed by other companies and they have been banned to hit the AppStore for some reasons. The applications mentioned here were released by Cydia, and they seem quite useful, but they are not available in the Apple App Store.
There is one aspect in which iPhone has only to loose, and this is video recording. This feature is not available on iPhone, unless you jailbreak it and install proper software. For this you can use utilities like Cycorder or iPhone Video Recorder. Another interesting aspect which can be achieved by jailbreaking the iPhone is that you can change the look, the theme, and you can feel more comfortable with your iPhone's new face. Winterboard is one application which can help you improve your smartphone's look, and here are some images with pimped iPhones.
This may not be the real reason for non-tech-geeks users of iPhone, but for the really interested persons in tweaking and improving iPhone might me interesting.
The inner part of the iPhone is a trim version of the well known Mac OS X, which is basically an Unix core. Are there available Unix applications which can be installed on the iPhone? The answer is yes, but only after jailbreaking it. After this, you can easily install applications such as Apache Web Server or any other Unix utilities. One server that most jail-broken iPhone users use is a SSH daemon. This SSH helps you to connect remotely to the iPhone and then transfer any files from/to it.
The last and the most common reason for jailbreaking the iPhone is unlocking it. To be able to unlock it, you have to pass through this stage of jailbreaking, so you can go further with the installations.