A story arc. This isn't unique to anime, but an element in most story telling.

Anime stands for Japanese Animation. An Arc is a story within a bigger story that features it's own prologue, rising action, climax, falling action, and epilogue. Typically as the story goes on the Climaxes of each successive arcs become bigger and bigger in scope. Anime has its own conventions for storying telling compared to American stories: typically as the story goes on the main character acquires a larger and larger supporting cast, the character becomes more powerful and the villains become so in turn.