i am confused on what it is

Certain species are "fabled":
Aeridini (only catchable in the wild in the Spring Festival Zone)
Lighira (only catchable in the wild in the Summer Festival Zone)
Ryori (only catchable in the wild in the Fall Festival Zone)
Griffi (only catchable in the wild in the Winter Festival Zone)
Ny'vene (not available in the wild but can be purchased in the Arena in the Vale)
Puffadore (not available in the wild but can be purchased in the Vale)
Nephini (only catchable in the Festival Zones and once you get to the Vale).

They all have 7 day cool down periods for breeding.

Just to say, Puffadore's aren't actually fabled, merely only typically attainable from their shop, making them an outlier amongst 'common' pets.

This can be detarmined by the base stats of a given pet: Fabled pets have higher base stats compared to common pets obtained the same way. (also, if one looks in the Generator's List of Species, Fabled Pets have their nature noted beneath their species name)

(to demonstrate, let's grab a couple of our level 0 pets:
Tamed commons have ~11 average in their base stats whilst tamed fabled pets have ~22.
Exclusive (those that are created) commons have ~22 base, while Exclusive fableds have closer to averaging 40)
(pets generated with essences also have their own base stat averages depending on the type, but whatever)

thank you