'annates' originates from Medieval Latin 'annatae' (or late Latin 'annata'), ultimately from Latin 'annus' meaning 'year' (through 'annata' meaning 'a year's sum or revenue').

'annata' in Medieval/Latinate usage (meaning a year's revenue) entered medieval ecclesiastical and legal vocabulary and became Middle English 'annates', used for the payments of the first year's profits of a benefice.

Initially it referred generally to a year's revenue ('a year's payment'); over time it came to denote specifically the first year's profits of an ecclesiastical benefice paid to the papacy (and by extension the payment itself).