From the Super Mario Wiki, the Mario encyclopedia
The Outback mayor is a monocled, moustached Mushroom Person who inhabits the Outback, a town in Down Under Land, which he is the mayor of. As Down Under Land is similar to Australia in many aspects, the Outback mayor speaks with a rather fitting accent.
The Outback mayor only ever appears in The Super Mario Bros. Super Show! episode "Crocodile Mario". When Kangaroo Koopa steals the Magic Statue that protects the Outback, the Outback mayor asks for Mario, Luigi, Princess Toadstool and Toad to stop him, but they arrive too late. He then informs them that the town has become vulnerable to the crocodiles, and tells everyone that the only place that they can be safe from the crocodiles is on top of the town's general store.
The Outback mayor exclaims that the only way for Mario and Luigi to save the town is to reclaim the stolen Magic Statue from Kangaroo Koopa. As Mario and Luigi flee from the Outback to retieve it, the Outback mayor awaits their returned along with Princess Toadstool, Toad and the rest of the townsfolk.
After the crocodiles had chew up most of the general store, the Outback mayor directs everyone to take refuge in the branches of a nearby tree, where they wait while the crocodiles begin to chew away at the trunk. Mario and Luigi eventually return with the Magic Statue, and with it, the crocodiles are scared out of town, chasing Kangaroo Koopa as they flee. Laughing at Kangaroo Koopa's defeat, the Outback mayor thanks Mario and Luigi for saving his town.