When you find and incubate eggs you will unlock a pet that will help you in the game by attacking prey and giving you bonuses such as increased health or increased speed. You will be able to tell how useful a pet will be by the rarity it is given, the rarer the pet the better. There are 3 different types of eggs, the rarest being the Golden Egg.
Standard Eggs
These can be found once per game and after the incubation period they will reward you pets for your dragons.
Premium Eggs
These eggs can only be purchased. They are instantly opened and there is no incubation period.
Golden Eggs
The only way you can unlock Special Pets is through collecting Golden Egg fragmennts which you will get each time you open an egg and recieve a Pet you already have. After you have a certain amount of Golden Egg fragments you will be rewarded a Golden Egg.