What happens after I buy eggs?

Once you buy an egg, it is put in your Hatchery where it is kept to hatch (eggs take 1 week to hatch). Once it hatches into a bird, your newly-hatched bird is transported to your birdhouse where it begins to lay eggs for you which you can sell for coins (you'll receive notifications at every point, and you can always check on your eggs in your Hatchery).