In the US, "Assistant Professor" is a junior rank among permanent university faculty. Generally, Assistant Professors are independent researchers with more or less the same job responsibilities as more senior faculty (Associate Professors or Full Professors), but without the perks of tenure. That is, they teach classes, advise graduate students, apply for grants, and have administrative responsibilities. (In other countries, the term may have a slightly different meaning. It is roughly equivalent to a Lecturer in the UK system.)
As far as I know, Assistant Professors are not assistants to anyone. So why the name?
Usually an Assistant X is someone who works under the supervision of X and helps X carry out their duties, but that is not the case here. In contrast, other university titles containing "Assistant", such as "Research Assistant" or "Teaching Assistant", do fit the more conventional definition of the word.
After a bit of searching, I have not been able to find any information about the origin of the term. Although it has apparently been in use since 1827. Does anyone know more about the history of the term?
Perhaps the job has evolved from a true assistant position into what it is today while the title has remained the same. Alternatively, it may be a (mis)translation or the meaning of "Assistant" has changed. If someone can find a source documenting a history like that, I would happily accept that as an answer.