Favorite star is at the top right corner of the screen showing details of Pokemon. Starred Pokemon cannot be transferred to Professor Willow. It is very easy to add or remove the star. This page notes how to prevent transferring your favorite Pokemon unintentionally by the function.
There are two ways to add a star to your favorite Pokemon. Both either ways are very easy and shown below.
Your Pokemon also have the star in your Pokemon storage.
If you try to transfer starred Pokemon, the message 'Cannot transfer a favorite Pokemon!' pops up.
