The Shadow Arena is located within the Shadowlands and connected to the Factory by an underground tunnel. The arena is used by the Shadow Lord to put his prisoners up against its evil creatures, most of the time killing them. They mostly fight against vicious Vraals, the Shadow Lord's personal fighting beast.
The Shifting Sands
After taking control of the Rithmere Games, the Shadow Lord used the Games to find new combatants for the Shadow Arena. All finalists and semi-finalists were captured after the Games and carted to the Shadowlands to fight Vraals in the arena.
Lief, Barda, and Jasmine were captured by two Grey Guard and overhead them talking about the Shadow Arena.
The Valley of the Lost
Doom explains to Lief, Barda, and Jasmine how he escaped from the Shadow Arena and made his way back to Deltora. 
In the Deltora Quest anime the Shadow Arena is depicted as a large round metal cage and are shown to have columns that circle the inside of it, which is where the audience (mostly Grey Guards and Ols) is seated and watches the brutal fights.
The Arena is most likely inspired by the gladiatorial fights hosted at the Colosseum and amphitheaters of ancient Rome.