Translation administrators are users who have the technical ability to mark pages for translation using the page translation functionality that is part of the Translate extension. In addition to that, they are the only ones that can delete the translated pages created by the translation extension.
Meta administrators are able to add (and remove) themselves to the group if they are willing to help other users or need it and they know what to do (because they've read the documentation and if possible tested it — Meta is not a playground and translators are not toys). Additionally, any user can request it (with the same requirements) to local bureaucrats at Requests for adminship. Bureaucrats are also able to remove the right.