'assn' originates from English, specifically as an abbreviation of the word 'association', which ultimately comes from Latin 'associatio' / 'associare', where 'ad-' (or assimilated form 'as-') meant 'to/toward' and 'socius' meant 'companion, ally'.

'association' passed into English via Old French/Latin: Latin 'associatio' (from 'associare') → Old French/Medieval Latin forms → Middle English 'associacioun' and eventually modern English 'association'. The written abbreviation 'assn.' developed as a clipped form used in notes and addresses.

Initially it referred to the action or state of being associated ('joining, uniting'); over time it also came to refer to a concrete organized group of people ('an association' as an organization).