They were used in the past to denote the rarity and power level of dinosaurs.
Golden stars: These were for non-hybrids. Commons start of with no stars and gain one more each time their level cap increases (i.e L10 to L20). Rares start of with 1 star, Super rares with 2 stars and Legendaries/Tournament with 3 stars. Therefore the max number of golden stars a dinosaur can have is 6 (L40 Legendary/Tournament).
Purple stars: They are the same as the golden stars although just for hybrid dinosaurs. And so the max number of purple stars a dinosaur can have is 6.
Although it’s irrelevant now, I still use it as a gauge to choose which dinosaurs to use in the various tournament leagues. Hope this was easy enough to understand.