A marathon was a long-distance running race. By the 24th century, Starfleet Academy had an official marathon run by its cadets.
In 2366, Devinoni Ral told William T. Riker that "the last mile of the marathon is always the toughest", referring to ongoing negotiations over the use of the Barzan wormhole. (TNG: "The Price")
The term could also be used to describe a prolonged period of a particular activity. In 2375, Neelix mentioned allowing Tom Paris to replicate pork rinds for his monster movie marathon. (VOY: "Warhead")