A story arc is a recurring overall plot line that spans more than one episode. On Futurama, numerous story lines appear in several episodes and develop further on this plot, but may have been completely absent in the episodes immediately prior and succeeding these episodes, and sometimes even have gaps in between.
Story arcs are generally used by the writers to explain character backgrounds or used to explain the relationship between two characters, such as the Fry-Leela relationship, which occurs over several episodes.
Futurama is fairly unique among animated shows for its use of these overlying story arcs and continuity. In Futurama, things that occur early in the series can have an impact on later events.
Other examples include: