A personal database was a database kept by an individual for personal use.
Everyone on USS Voyager had a personal database. In 2375, after learning from Neelix of the existence of an image depicting Chief Engineer B'Elanna Torres with her foot caught in a plasma injector, Tom Paris was eager to see it and possibly send it to everyone else's personal database. Torres threatened she would kill him after she finished deleting The Doctor's holoprogram - he being the one who had taken the image. (VOY: "Nothing Human")