A cadet is a rank or title, usually assigned to service organization personnel attending an educational institution oriented towards training officers for military, paramilitary or service organizations, such as a navy, pilot corps, or police or peace officers.
History and specifics
In the Federation, the term is most commonly used to refer to Starfleet students at Starfleet Academy. In that context, it is synonymous with "midshipman", with the latter variation reserved for those cadets who are assigned to active duty or training missions. (ST movie, novelization & comic adaptation: The Wrath of Khan)