Breeds that are considered as hard feathered chickens are generally the 'Game' varieties such as Indian Game, Modern Game, Old English Game Bantam, Oxford Old English Game and Asil. They have a distinctive upright body shape as well.
When we refer to a chicken being hard or soft feathered it is a general reference to the stiffness of the feather shaft. A soft feathered hen will have a lot more fluffiness to the bottom of each feather giving her a more fuller look than a hard feathered one.
When looking at a soft feathered hen from behind you could say that she has a petticoat looking bottom because she is so fluffy. That fluffiness may not be all over her body like the Silkie breed, but she has a looser look to her feathers.
Hard feathered poultry does not have the fluffiness but has sleeker lines. Typically their wing feathers meet neatly around near their rear rather than having the petticoat look of a soft feather chicken.
To understand more about which chicken breeds are hard or soft feathered or true bantams, check out The Poultry Club of Great Britain's website for more details in picture.