Basic training was an introductory program for new recruits into a service.
In 2154, T'Pol expressed her interest in possibly formalizing her Starfleet service, upon which Jonathan Archer suggested he could use his influence to help her skip basic training. (ENT: "Countdown")
In 2374, Kathryn Janeway surmised that Chakotay's fight with a simulated Vori commandant moved him up from basic training to an actual fight. (VOY: "Nemesis")