Thestral

Thestrals are fictional winged horses introduced in the novel Harry Potter and the Order of the Phoenix.

Warning: Spoilers follow

They can only be seen people who have seen a death, and even then only after the death sinks in to become an established fact in their minds. Often what follows the immediate death is denial.

Thestrals pull carriages at Hogwarts up to the school invisible to most students. Prior to Harry Potter and the Order of the Phoenix, Harry and his friends(and readers) assumed that the carriages were bewitched to move on their own. After Harry Potter saw Cedric Diggory die at the end of Harry Potter and the Goblet of Fire, he could see thestrals. Luna Lovegood saw her mother die when she was nine, and has been able to see the thestrals since she arrived at Hogwarts, and assumed that everybody else could as well.

Care of Magical Creatures students learn about thestrals in their Fifth Year. In Fantastic Beasts and Where to Find Them, thestrals are mentioned in the winged horse entry.