In a nutshell, it enables developers to create code packages that can be toggled on and off without the end user having to restart their browser. This is something that cannot be done with Firefox's current add-ons system, but has been possible in third-party tools such as Greasemonkey, which allow users to pick and choose which scripts are active.
It solves another annoyance by letting developers create code that isn't outdated or broken every time the browser gets a major update. This is a problem that has plagued Firefox add-ons for years, and forces developers to make small tweaks or changes to get their extensions up and running--even if they've long since stopped working on a particular extension. Under this system, whatever Jetpack add-ons you have installed will still work. At least that's the promise.
In the introductory video of Jetpack (embedded below), Aza Raskin, who is head of user experience for Mozilla Labs, shows what the tool is capable of. In the first part, it's a simple ad-blocking tool that users can toggle on and off to keep the browser from loading certain page elements from ad providers. In the second half, he demonstrates how custom code can do the same thing to other page elements, depending on what developers have coded into any one particular Jetpack module.
Besides no restarts and no breaking with updates, the most exciting aspect of Jetpack is how it can give users more control over what they see on a site, and how they can interact with its content. Like Ubiquity (another Mozilla Labs project), it also appears to be putting these add-ons right in the hands of users as soon as they visit a site with Jetpack controls, which means there's less of a need to promote it in an add-ons directory to have users find it.
Raskin warns that at version 0.1, the project is still a little rough. You can try out a few code samples, and read more about how to get involved, on the Jetpack developer site.