clientyoudaoicibaDictYouDict[client 词源字典]
client: [14] The original status of a client was rather lowly: he was someone who was at another’s beck and call, and dependent on them. The word comes from Latin cliēns, an alteration of an earlier cluēns, the present participle of the verb cluēre ‘listen, follow, obey’; hence someone who was cliēns was always listening out for another’s orders, unable to take independent action (in ancient Rome it meant specifically a plebeian under the protection of a nobleman).

That sense is preserved in such English expressions as ‘client state’. The word’s more modern senses have developed through ‘person on whose behalf a lawyer acts’ in the 15th century to simply ‘customer’ in the 17th century.
[client etymology, client origin, 英语词源]
client (n.)youdaoicibaDictYouDict
late 14c., from Anglo-French clyent (c. 1300), from Latin clientem (nominative cliens) "follower, retainer," perhaps a variant of present participle of cluere "listen, follow, obey" (see listen); or, more likely, from clinare "to incline, bend," from suffixed form of PIE root *klei- "to lean" (see lean (v.)).

The ground sense apparently is of one who leans on another for protection. In ancient Rome, a plebian under protection of a patrician (called patronus in this relationship; see patron); in English originally "a lawyer's customer," by c. 1600 extended to any customer.