'prophesy' originates from Latin and Old French forms ultimately from Greek. It goes back to Greek 'prophēteuein' (to act as a prophet), where 'pro-' meant 'before' and 'phēmi' meant 'to speak.'

'prophesy' changed through Late Latin/Old French forms (e.g. Latin 'prophetare' / Old French 'prophétiser') and entered Middle English as 'prophesien'/'prophesyen', eventually becoming the modern English 'prophesy'.

Initially it meant 'to act as a prophet or to speak for a deity,' and over time it has kept that sense while also extending to secular predictions of the future ('to predict'), so the core meaning remains forecasting or declaring what is to come.