'impassible' originates from Latin, specifically the Late Latin word 'impassibilis', where the prefix 'in-/im-' meant 'not' and 'passibilis' meant 'able to suffer (from patī, to suffer).'

'impassible' entered English via Late Latin 'impassibilis' (and via Old French forms such as 'impassible'), and eventually became the modern English adjective 'impassible'.

Initially, it meant 'not able to suffer' (especially of a deity); over time it retained that theological sense but has also taken on a broader sense of 'not emotionally affected' or 'unmoved'.