The ninth month of the Shire Calendar, following from Wedmath. Halimath was approximately equivalent to modern September, running from modern 23 August to 21 September in a normal year. This was a time of harvest, and the name Halimath or 'holy month' derives from the harvest offerings made at this time of year (in Bree, the connection to the harvest was made even clearer in their preferred name for the month, Harvestmath).
The month-name Halimath was ancient even to the Shire-hobbits, and derived from their early history when they dwelt in the Vales of Anduin. The name was evidently acquired from the Men who also lived in those vales, and a similar name for the same month was said to have been used among the Rohirrim, who descended from those same Northmen of the Great River's vale.
Old English Hāligmōnað represents a 'holy month', a time when offerings would be made from the harvest. The connection with harvest-time is even more explicit in the name for this month among the Bree-landers, who knew this month as Harvestmath. The same Old English element hali-, 'holy', appears in the name of the Halifirien, the 'holy mountain' in Rohan, far away to the south of the Shire.