'rehumidification' is formed from the prefix 're-' (from Latin 're-', meaning 'again') combined with 'humidification', which ultimately derives from Latin 'humidus' meaning 'moist'.

'humidus' (Latin) gave rise to medieval/late Latin forms related to making moist (e.g. 'humidificare'/'humidificatio'), which passed into English as 'humidify' and 'humidification'; the prefix 're-' was later attached in English to form 'rehumidification' meaning 'humidification again'.

Originally related to 'making moist' (humidification); with the addition of 're-' the meaning became 'making moist again' or 'restoring humidity'.