Task List/tutorial step1

Eggs need a lot of warmth to hatch, so they need to be held by interacting with them. Interact with other user's Pokémon to attract their attention and they may return the favour!

You can use the Users Online list at the top to find users to interact with. There are also links in the upper left corner, with which you can either find a user that has interacted with you, or an online user that has yet to receive any interactions from you.