After your Ranch reaches level 10 the Favorites option will be made available. With Favorites active, while hovering over a Pokémon so that its name appears, you can click on a circle that becomes a crown. This means that Pokémon has been chosen as a favorite.
The whole purpose of this is so that you can make the Ranch population only your selected favorites. To do this simply go to Deposit/Details and, in the green box in the top 1/3 of the screen, click until Favorites appears.
Also, by clicking the flag in the upper-right corner in Deposit/Details, you can start a parade that only includes marked favorites.
To remove this status simply click on the crown and the Pokémon will no longer be marked as a favorite.