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!
There are links at the top of the page that can help you find other users to interact with through the "... users online" or "Jump" links. Or, return the favour and click back those who have interacted with you through the "Today's interactions" and "Clickback" links!