Created by Lex Luthor from Metallo's heart, which he wore at all times to keep Superman away from him. Batman later aquired the ring, just in case Superman ever loses control of his powers.
Joe Coyne was obsessed with pennies, even beginning his criminal career by robbing a cash register filled with pennies. This giant penny is a souvenir of Batman's battle with Joe Coyne.
Sure, it isn't a trophy, but it's cool enough to be in the trophy room. It can literally find any information and pretty much do anything, from analysing DNA to tracing people across the planet.