The word intern as a word meaning "trainee who works to get experience" wasn't put in place until 1924. Since 1827, however, a different definition of "assistant physician" existed, and was applied because the helpers did internal work for hospitals. That came from French interne, which had the same definition but could also mean "internal", and eventually traces to Latin internus, "within". The root there is inter, which could also mean "among", and, further back, it (through Proto-Italic) derives from Proto-Indo-European hen, meaning "in". Use of the word intern over time peaked in the 1970s and the turn of the century, but has recently been decreasing for some reason. Fun fact: intern has a lot of dead definitions, including "of the soul", "boarding school student", and "the domestic affairs of a country".
Adam Aleksic, a rising sophomore studying linguistics and government at Harvard University, has been described as the internet's sixth most famous etymologist. He also has disturbing interests in politics, vexillology, geography, board games, conlanging, and law.