Coming-of-age films, as the name suggests, revolve around stories about passing from adolescence to adulthood. They are generally the cinematic form of the literary Bildungsroman genre, which focuses around moral growth and character change.
In the film medium this is usually focused around a protagonist (or small group of protagonists) and their mental growth. It can either centre around a singular event which helps propel this (such as a great shock, overcoming a harsh life event, learning an important life lesson, etc.) or can be a longer portrayal of multiple years of progress and growth. Boyhood (2014) is an example of the latter, following more than a decade of character growth.