An arc is the curved part of a circle. In reference to a TV series, and arc is a storyline that spans several episodes, usually ranging from 3 to 10-ish. For example, in Star Wars: The Clone Wars, examples of story arc include The Box Arc, The Citadel Arc, the Nightsisters Arc, and the Geonosis Arc. In short it's a mini-story that has a beginning and end, but is still part of a larger whole.