what does it mean if a pet is fabled? thanks, run879

It means the species is only available through certain means or times of the year.
Example, the Aeridini, Lighira, Ryori, and Griffi are only available during their respected times of the year, in order: Spring, Summer, Fall, and Winter festivals.
Nephini are only available during festivals but they're very rare.
PUffadore and Ny'vene are available year round but they require going to their respected shops and purchasing the eggs using the shop's used currency.

Fabled Sylesti females can also only breed every 7(?) days instead of the normal 3.

Their stats, as compared to other species, also tend to be a lot higher when generated or caught wild.

Just a slight correction to what Animela said.

Puffadores are not fabled pets, though they can't be found in the wild.
I'm assuming it's because they can be bought in gold from an NPC in the 3rd region, so it's not that hard to get them once you reach that stage, as compared to Ny'venes where you have to fight in the arena to get them. (Sort of how it's quite easy to get pets from the scale shop)

Another defining feature of fabled pets are that their eggs are unique. Like Aeridini eggs are flowers, Lighiras' have fur around the bottom, etc.

Edit: oh, and Nephinis are available all year round, but only in the 3rd region, and super rare