2. A group of adjoining mating territories of a species.
The Arena, More than a Place
The ancient Romans who watched the gladiators fighting to their deaths with swords and other weapons, or wild animals, killing and being killed, went to the amphitheaters for their "entertainment."
The ground couldn't soak up the quantities of blood spilled on it so the show producers covered the ground with absorbent arena (sand). The sand, or arena, became the name of the place for shows, then sports, etc.
Another version is, "To undertake a never-ending task."