Yarn is a new crafting material that is used when purchasing outfits. The number of yarn needed depends on the rarity of the outfit.
To use your yarn, go to your Hatchling collection. When you pick a Hatchling you would like to get outfits for, you can see how many yarns and coins are needed for crafting each outfit. To craft an outfit just click on the green button showing the price for the outfit.
Once you have collected all the outfits for the Hatchling, you can collect the reward chest from the top.