're-admit' is formed from the prefix 're-' meaning 'again' and the verb 'admit.' 'Admit' originates from Latin, specifically the word 'admittere' ('ad-' meaning 'to' or 'toward' and 'mittere' meaning 'to send').

'Admit' entered English via Old French 'admettre' and Middle English forms, evolving from Latin 'admittere' to Middle English 'admitten' and eventually to modern English 'admit.' The productive prefix 're-' (from Latin 're-') combines with 'admit' to form 're-admit' (also spelled 'readmit').

Originally 'admit' meant 'send to' or 'allow to enter'; over time it took on the more general sense 'allow entry' or 'accept.' 'Re-admit' thus means 'allow entry again' or 'accept again,' following the original core sense.