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The name currently in use is a fan designator; see below for more information.
Smoothness is a property of Berries in the Generation III and IV core series games. It affects the feel of Pokéblocks and smoothness of Poffins made from them.
Smoothness is unrelated to the purely non-functional firmness property which is visible on Berry tags; for example, while the Pecha Berry and Chesto Berry both have a smoothness of 25, the Pecha Berry is Very Soft while the Chesto Berry is Super Hard. Smoothness is not directly visible in-game.
Pokéblocks and Poffins
The feel or smoothness of a Pokéblock or Poffin is equal to the average smoothness of the Berries used minus the number of Berries used, rounded down. This is equivalent to the following expression (where n is the number of Berries used):
( ( Smoothness1 + ... + Smoothnessn ) / n ) - n
When a Pokémon eats a Pokéblock or Poffin, that food item's feel or smoothness is added to the consumer's sheen, up to a maximum of 255. A Pokémon with 255 sheen cannot eat any more Pokéblocks or Poffins in the Generation III and IV games (in Pokémon Omega Ruby and Alpha Sapphire, Pokéblocks are not affected by sheen).
List of Berries' smoothness