is that Latin was used in Europe for official things all through the Middle Ages.
See the OED (Etymology Online):
c. 1200, terme "limit in time, set or appointed period," from Old French terme "limit of time or place, date, appointed time, duration" (11c.), from Latin terminus "end, boundary line," in Medieval Latin "expression, definition," related to termen "boundary, end" (see terminus). Old English had termen "term, end," from Latin. Sense of "period of time during which something happens" first recorded c. 1300, especially of a school or law court session (mid-15c.).
The meaning "word or phrase used in a limited or precise sense" is first recorded late 14c., from Medieval Latin use of terminus to render Greek horos "boundary," employed in mathematics and logic. Hence in terms of "in the language or phraseology peculiar to." Meaning "completion of the period of pregnancy" is from 1844. Term-paper in U.S. educational sense is recorded from 1931.
The 'terms of a contract' as in a 'limiting condition' came in the early 14th centure, it seems derived from the Greek 'horos' (see above).
And then you've got all these things with 'terms' like 'come to terms', 'be on good/bad terms with', etc.
Not all that peculiar, when you think about it, although I can imagine it's confusing for people who come from places where Latin wasn't used.