Sometimes, users when try to do something with their Pokémon, they come across with that the Pokémon is busy. Busy Pokémon can not be traded nor released and they may not do something else in some cases.
Situations when a Pokemon is Busy
Up in GTS
The Pokémon is set up in a trade or offered on the Global Trade Station. They can be removed from a trade at any time.
Up in Wonder Trade Station
The Pokémon is set up in a trade or offered on the Wonder Trade Station. They can be removed from a trade at any time.
In a Battle Team
The Pokemon is added in a Battle Team. They can be removed from the Battle Team at any time.
Set up in an Auction
The Pokemon is set up in an Auction. Unfortunately, auctions cannot be cancelled. The only way of getting the Pokémon is bidding on it.
The Pokemon is rumbling and cannot leave the area it is exploring. You will need to wait for it to come back.
The Pokémon is in the Daycare, and will not leave your box/party. The Pokémon is busy until you take it out of the Daycare.
In the Salon
Your Pokemon may be in the Salon.
Your Pokémon is currently on your HeroWalker.