Gladiator Trophy is one of the Items in Mobius Final Fantasy, used as an Arena Tournament prize, to unlock various areas holding Ability Tickets, Crystals, Summon Tickets and other items during those events. Like all Trophies, these are tied to their specific Special Event Regions, and cannot be used in other places -- even between Arena events.
First use was for the Infinite Arena, where Trophies were handed out in large quantities to unlock the prize areas. Up to 100x were needed per unlock.
Second use was for the Inferno Arena, where they were handed out in much smaller quantities, but required requisitely less of them to unlock similar prize-bearing areas. Up to 12x were used for any single unlock.