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Ubuntu provides four different software repositories, all of them official -- Main, Restricted, Universe, and Multiverse. Main and Restricted are fully supported by Canonical, while Universe and Multiverse don't receive the support you might expect.
On older versions of Ubuntu, only the Main and Restricted repositories were enabled by default. Ubuntu desktop systems now come with all four repositories enabled by default.
Main - Officially Supported, Open-Source Software
Main is described as "Canonical-supported free and open-source software." Canonical is Ubuntu's parent company, and they provide official support for all the software packages in Main. Every open-source software package included in Ubuntu's default installation is included here. Other important packages -- server software, for example -- are also part of Main.
Canonical supports packages in the Main repository with security updates and other critical fixes for the lifetime of the Ubuntu release
The Main repository is the main Ubuntu repository. If a package is in here, Canonical has committed to supporting it with security patches and other critical updates for the lifetime of the distribution. When Canonical boasts Ubuntu LTS will receive security updates for five years, it's the packages in the Main repository that will actually receive those updates. These are all open-source software, which means Ubuntu's developers can fix problems in them on their own.
You can spot packages in Main in the Ubuntu software center. They'll have the "Open source" license, and will state that "Canonical provides critical updates" until the end-of-support date for your installed release of Ubuntu.
Restricted - Officially Supported, Closed-Source Software
The Restricted repository contains closed-source software that's officially supported by Canonical. This only includes hardware drivers at the moment. Some Wi-Fi hardware needs closed-source drivers or firmware to work. Gamers need the NVIDIA or AMD Catalyst (formerly known as "fglrx") graphics drivers for optimal graphics hardware performance. These drivers can be enabled from the Additional Drivers tool in Ubuntu.
Canonical will officially support these closed-source drivers and firmware packages for the length of the Ubuntu release. They're committed to keeping these drivers working, fixing any big problems, and plugging any security holes. Canonical can't do this on their own, of course -- they have to wait for the hardware manufacturer to release new and updated driers when there's a problem. The code isn't open, so Canonical can't fix it on their own. That's why only critical hardware drivers are included here -- no other closed-source software is officially supported.
You can spot Restricted software by looking for the "Proprietary" license and the line "Canonical provides critical updates supplied by the developers" line. Canonical can't fix the drivers on their own -- they'll just provide important updates to you when they get them.
Universe - Community-Maintained, Open-Source Software
The vast majority of the software in the Ubuntu Software Center comes from the Universe repository. These packages are either automatically imported from the latest version of Debian or uploaded and maintained by the Ubuntu community.
Canonical does not provide official support or updates for these packages. An Ubuntu LTS release might be supported for five years, but the packages in the Universe repository aren't officially supported at all. They're generally fine, but they're not guaranteed to receive security updates. If a security update is found, these packages may never receive it until the next release of Ubuntu when a newer version of the package is automatically pulled in.
This shouldn't scare you away from installing software from Universe. This usually isn't a concern -- crucial desktop applications like Firefox are part of Main and will receive critical updates. If there's a huge problem, the Ubuntu community can fix a hole and roll out a fix. The community is exactly what it sounds like -- Ubuntu users and enthusiasts who aren't employed by Canonical, but who devote some of their time to working on Ubuntu or maintaining specific packages.
However, on a server system, it's worth considering whether the server software you install is part of Main or Universe. If it's from the Universe repository, you may need to keep an eye on security updates. You may have to update the server software on your own if a hole is found.
You can spot Universe software by looking for the "Open source" license and the line "Canonical does not provide updates... Some updates may be provided by the Ubuntu community." Canonical uses the word "may" here -- there are no guarantees!
Multiverse - Unsupported, Closed-Source and Patent-Encumbered Software
Multiverse is the place for questionable, controversial stuff. This includes closed-source software like the Adobe Flash plug-in and packages that depend on closed-source software, like plug-ins for Skype. It also includes open-source software with legal restrictions -- for example, audio and video playback software that infringes patents. DVD playback software isn't included here -- there are serious legal issues around the open-source libdvdcss DVD playback library. In fact, libdvdcss appears to be illegal in the USA.
Ubuntu can't officially distribute these packages along with the main distribution, but they're provided here for your convenience. On other Linux distributions, the stuff here is often found in third-party repositories you have to go out of your way to find -- RPM Fusion for Fedora, Packman for openSUSE, and Penguin Liberation Front (PLF) for the defunct Mandriva distribution.
As with the Universe repository, Multiverse is a community-supported repository. There's no guarantee of security updates here. Because so many of the packages are closed-source, the community often couldn't fix problems you encounter even if they wanted to.
You can spot these packages by their "Unknown" license. As with Universe, the Ubuntu Software Center states the Ubuntu community may provide updates, but Canonical won't.
On a typical home PC, you shouldn't worry about these differences too much. Packages you install from Universe should generally be pretty secure -- if there is a big problem, the Ubuntu community can deal with it and roll out a security update for you. Packages from Multiverse may be necessary for viewing some types of multimedia files and even viewing Flash content in Firefox.
On a server or a critical workstation, these differences are more important. Install software from Universe and you're not guaranteed support from Canonical for it. This is a big deal if you're exposing that software to the Internet on an Ubuntu server.