're-immerse' originates from the prefix 're-' (from Latin) and the verb 'immerse', specifically Latin 'immergere', where 're-' meant 'again' and 'mergere' meant 'to plunge or dip'.

'immerse' changed from the Latin word 'immergere' (literally 'in-' + 'mergere') through Old French/Medieval Latin forms into Middle English 'immerse', and the modern English verb 're-immerse' is formed by adding the productive prefix 're-' to that verb.

Initially, the root meant 'to plunge into or sink'; over time it came to be used both for literal plunging and figurative senses of 'involving deeply', and 're-immerse' now means to do that action again (literally or figuratively).