Limbo
The term Limbo is used to describe an avatar or other atoms being unassailable by players or servers. The most common symptom is that the loading screen never ends when attempting to login on an avatar. Solar systems can also go into limbo, making them stop responding to the server and any spacecraft or avatar that enter that solar system will be stuck until the solar system's server is restarted.
The loading screen can also some times be referred to as "the limbo screen".
Technical
The original version of limbo was fixed at some point in 2014, but the term is still wide used whenever someone is unable to login on their avatar.
Now a days however, the cause of limbo is due to a server crash. The servers are all running in GDB, which causes them to lockup and wait for inspection before being able to resume. This helps a lot with fixing server crashing bugs.
When a server crashes, all the solar systems that that server was handling will freeze. All atoms in those solar systems will stop responding and all atoms entering any of those systems will also freeze.
Help
If you are unable to login on an avatar, it is most likely a problem with the server that is handling the solar system.
The first thing you'd want to do is alert Haxus. This is done by posting in the "limbo" thread on the forum, this thread is monitored extra carefully by Haxus so he can fix the servers when they lock up.
History
Before being fixed at some point in 2014 it was common for avatars to become stuck in "limbo" when transiting from one server to another. This was due to errors in the server-side miscommunication, making it so that an avatar was not on any server at all.