Two days in the calendars of the Hobbits that marked the end of one year, and the beginning of the next. On a modern calendar, they fell on the 21 and 22 December3. Around them, the six-day festival of Yuletide was held, running from 29 Foreyule to 2 Afteryule.
Due to a peculiarity of the Shire Calendar, the Yuledays always fell on the same days of the week. The last day of the year, 1 Yule, was always a Highday (Friday), while the first day of the following year, 2 Yule, was always a Sterday (Saturday).
The formal use of Yule in the Shire calendar cannot, by definition, predate the foundation of the Shire in T.A. 1601. However, its appearance there represents a survival of an older tradition, and the name 'Yule' for a midwinter festival was known as far from the Shire as Rohan and Gondor.
However it's possible that it derives from a form of Northern Mannish and later used in Rohirric. Since Gondorians of the Third Age were in part Northmen, the word was recogniseable as a 'northern name' for the midwinter festival.