From the Super Mario Wiki, the Mario encyclopedia
Fryguys are living flame creatures that were once Mushroom People. Though only one Fryguy, aptly named as such, ever appeared in one Mario game (Super Mario Bros. 2 and its subsequent remakes), the species of Fryguy were featured quite prominently in Nintendo Comics System.
Unlike the Fryguy of Super Mario Bros. 2, who was created through the magic of Wart, the Fryguys of Nintendo Comics System are created in a much different way; according to the story "Beauty and the Beach", once a Mushroom Person is exposed to extreme amounts of heat, it will metamorphose into a Fryguy, becoming increasingly destructive and dangerous.
Fryguys often appeared as shock troops of King Bowser Koopa, with several Fryguys often shown to his bidding in stories such as "The Fish That Should've Gotten Away". Despite dozens of Fryguys being seen though, mentioning of a shortage of them were once made by Bowser in the aforementioned comic "Beauty and the Beach", which had Bowser trying to make a volcano erupt in order to douse hundreds of Mushroom People in lava, thus making more Fryguys.
Several mentions of schools made specifically for Fryguys have also been made; some of these include Fryguy High (which later burnt down) and the Fryguy Kindergarten, which acted as a trap hidden under the throne room of Bowser's Castle.
Though Fryguy himself was the only Fryguy character to actually appear on The Super Mario Bros. Super Show!, the fact that he was a member of a species of creatures, instead of a unique entity, was hinted at in some of the show's episodes, most notably in "Hooded Robin and His Mario Men", as Princess Toadstool's idea of distracting Fryguy, was a "Frygal". Also during the episode "Raiders of the Lost Mushroom", Toad, Mario, Luigi and Princess Toadstool referred to the Fryguy that chased them as a Fryguy, implying that the Fryguy character wasn't the only member of his own species.