The choices on the Updates screen in the Software Sources application (System -> Administration -> Software Sources) are not explained in the components section of the official documentation. This wiki page tries to fill in that gap.
Important security updates
These are obviously the only ones you will have to enable if your computer is connected to the Internet, in order to keep you secure.
Enabling this is smart. Even if you don't connect to the Internet, it won't hurt.
These updates contain non-critical updates which can remove major annoyances and broken packages, but which do not affect your security. Other than fixing some, they do not enable any features.
Enabling this is generally a good idea. The amount to download as well as the changes are not too big, but it improves your system stability in various ways.
Enabling the proposed updates repository can break your system. It is not recommended for inexperienced users.
The proposed updates are updates which are waiting to be moved into the recommended updates queue after some testing. They may never reach recommended or they may be replaced with a more recent update.
Enabling this is reasonable if you want to participate in testing minor updates, or know that your specific problem has been solved here but the package hasn't reached recommended yet.
Backported updates are pieces of software which come from a newer major release. Thus, they can contain new features, but may also break compatibility with their older version. However, they are compiled specifically for your version of Ubuntu. In effect it saves you the hassle of broken dependencies and major downloads.
Enabling this is reasonable if you want new features but don't want your system to be unstable.
Read more in UbuntuBackports.