From Latin 'improvisus' (unforeseen) — to improvise is literally to act without having 'seen ahead,' from PIE *weyd- (to see).
To create or perform something spontaneously without preparation; to make do with whatever is available.
From Italian 'improvvisare' (to sing or speak extempore, to compose on the spot), from 'improvviso' (unforeseen, unexpected, sudden), from Latin 'imprōvīsus' (unforeseen, not seen beforehand), composed of 'in-' (not) + 'prōvīsus' (foreseen), past participle of 'prōvidēre' (to see ahead, to foresee, to provide for), from 'prō-' (before, ahead) + 'vidēre' (to see), from PIE *weyd- (to see, to know). To improvise is literally 'to act in a way that was not foreseen' — to perform without having seen ahead. The PIE root *weyd- is one of the great knowledge roots, producing
The Italian tradition of commedia dell'arte, where actors improvised dialogue around stock characters and loose plot outlines, gave rise to the modern word 'improvise.' These performers were called 'improvvisatori' — people who acted 'without foresight,' the negation of the Latin 'prōvidēre.'