Conscription, or being drafted, was the act of forcing someone to enlist in a military, often without their consent.
In the 2270s, an upset Doctor Leonard McCoy protested his reinstatement under the reserve activation clause, clarifying "in simpler language, Captain, they drafted me!" (Star Trek: The Motion Picture)
In 2373, Neelix asked Kathryn Janeway's permission to accompany a rescue team that was trying to locate Kes, giving his combat training and willingness to make the mission a success as reasons why he ought to go. She agreed, saying "Consider yourself drafted." (VOY: "Warlord")
In 2374, the Vori Defense Contingent actively maintained dozens of training facilities that were used to conscript their own people, as well as any aliens they were able to capture, to assist in their war with the Kradin. (VOY: "Nemesis")