Demon peppers are a type of very spicy pepper that can be only handled by flame Demons. It is also an ingredient of Scorched Alaska that makes it unbearably hot. It could also substituted by a hot poker, as demonstrated by Guybrush.
The LeShip cook/chef Putra had a pepper shaker containing it. In the harder game mode, the shakier would be empty at first but would be replaced by a full shaker sometime after heading to Monkey Island.
Guybrush would make use of it by adding the demon pepper to some fish in order to get rid of a bird holding one half of his portrait with Elaine.