A training arc is a stretch of story devoted to preparation: a character or team training under a mentor, regime, or camp to gain a skill, form, or level they will need. It is the process counterpart to the power-up's payoff.
The training arc runs on a simple contract: the audience watches the work, so the work counts. Its scenes are built from regimen and measurement: drills repeated until they change, a technique broken into steps, a benchmark rival or record that converts effort into a number. The genre's great training arcs are remembered as fondly as its battles because anticipation is a pleasure of its own.
It also does quiet narrative labour. Training is where rules get taught without a lecture, where mentors and rivals deepen, and where a series can breathe between climaxes while still moving its power scale. Spokon built the form; battle shonen inherited it whole.
The failure mode is famous in the other direction: growth asserted without process, a power-up granted by declaration. Fans' loyalty to the training arc is really loyalty to earned change, and it is why this site's canon sheets log the major training periods of a subject: they are where the facts about who can do what are actually established. Sports science gives modern training arcs their flavour: periodization, film study, and recovery days appear on screen because the audience now includes athletes who would notice their absence.
In use"A summer of drills, one new technique mastered, and a rematch waiting at the end: that is a training arc."