Hay Day feathers are a product that is produced by using the Duck Salon in the fishing area.
This product came to Hay Day on the December 2014 update and is used in a couple new products including the Hay Day pillows.
Of course, you get the feathers from the ducks in the fishing area and they are unlocked at level 50.
To get the feathers from the ducks you catch you have to put them in the new Duck Salon and wait. The Hay Day Duck Salon is unlocked on level 51 and costs a lot of money to build.
Hay Day has not released yet on how long we have to wait for the ducks to be in the Duck Salon before we get the feathers but we do know it will be awhile.
However, once you have the feathers you can use them to create other products on Hay Day.