In Faerie Solitaire you can find, while playing, some eggs that you can hatch into various pets. You can make one of those as your active pet and let it gain experience, then let it evolve into its adult form. Once they're adults there's nothing else you can do with them, so you can choose another active pet and start again. Do they have any purpose other than being a side-game?
No, the pets in the game have no other purpose than to add a bit of replay value in terms of collectibles. They have no bonuses and their location is completely random, which can make trying to get that last egg rather frustrating. They're mostly there to add some more flavor to the game and as more incentive to replay.
The developers have stated that Faerie Solitaire 2's pets will have ingame functionality in contrast to the first game's pets.