English 'semester' was borrowed from German university terminology, which took it from Latin 'sēmestris' (six-monthly), a compound of 'sex' (six) and 'mēnsis' (month) — both traceable to PIE roots shared by English 'six' and 'month.'
A half-year term in an academic calendar, typically lasting about fifteen to eighteen weeks.
From German 'Semester,' from Latin 'sēmestris' (of six months, half-yearly), from 'sex' (six) + 'mēnsis' (month). The compound literally means 'six-month.' German universities adopted the term for their two annual academic periods (Wintersemester and Sommersemester), and English borrowed it from German academic usage in the early nineteenth century. The Latin etymon reflects a time when the Roman calendar year was organized around six
Both elements of 'semester' have English cognates hiding in plain sight: Latin 'sex' (six) is cognate with English 'six' (from PIE *swéḱs), and Latin 'mēnsis' (month) is cognate with English 'month' and 'moon' (from PIE *meh₁n̥s-, the moon that measures months). So 'semester' is etymologically 'six months' — and 'six' and 'month' are the same words in their English and Latin forms, just disguised by three thousand years of sound change.