An archaic form of the name of the last day of the week in Middle-earth. Etymologically, it descended from the ElvishValanya, 'Day of the Valar', so the element Hih ('High') refers to the High Ones of Arda and their kind. Though its name is conventionally translated as 'Friday', as the last day of the week Hihdei was actually more akin to modern Sunday. It was considered the 'chief day' of the week, and its afternoon and evening were traditionally given over to leisure and festivities.
Note that Hihdei is the original form specified by Tolkien, but many editions of The Lord of the Rings spell this ancient name as 'Highdei'.