In the U.S., selective service is the formal term for the draft, or required military service. The last time selective service was used this way was during the Vietnam War.
The federal agency that's responsible for keeping a list of people who are eligible to serve in the military, and for drafting them if necessary, is the Selective Service System. Selective service means being selected to serve, a gentler way to think about being required to fight in a war. Even today, when an American man reaches the age of 18, he is legally obligated to register for selective service.