Psychic hoods allow a Space Marine Librarian to nullify an opposing psychic's power. Declare that you'll use the psychic hood after an opponent has successfully made a Psychic test, but before they have used the power. Each player then rolls a D6 and adds their model's Leadership value to the score. If the Space Marine Librarian beats the opposing model's score then the psychic power is nullified and may not be used that turn. If the opposing model's score is equal or higher, it may use its psychic power as normal.
Errata — Chapter Approved: Codex: Space Marines Q&A (v3.0): A Psychic Hood may only be used to counter enemy psychic abilities that require a successful Psychic test to use — it will not work against Warlock abilities and some Tyranid abilities. It can be used to counter any ability that requires a Psychic test as it is cast, even if that test is automatically passed.