The purpose of Jailbreaking an iPhone is to allow for third party applications that are not distributed through the Apps Store. When you jailbreak a phone, it generally works just like it did before, except that you have one or two additional applications (Installer.app and Cydia) on the home screen that are involved in managing third-party software. The apps let you find, download/install, update, or remove the third-party software.
The reason for jailbreaking the iPhone traditionally was that it was the only way to install third-party software. With 2.0, that reason partially goes away because Apple provides a way to install software.
On the other hand, the reason you might want to jailbreak the iPhone under 2.0 (3G or EDGE) is because there are things third-party software that are installed using Installer.app and/or Cydia can do that App Store apps presently cannot. They aren't limited by Apple's SDK limitations and can do more things (such as do more functions in the background while not activated, modify basic phone behavior, etc) and/or things that Apple might not allow in the store (e.g. programs to allow you to use any song as a ringtone, etc).