public (adj.) Look up public at Dictionary.com
late 14c., "open to general observation," from Old French public (c.1300) and directly from Latin publicus "of the people; of the state; done for the state," also "common, general, public; ordinary, vulgar," and as a noun, "a commonwealth; public property," altered (probably by influence of Latin pubes "adult population, adult") from Old Latin poplicus "pertaining to the people," from populus "people" (see people (n.)).

Early 15c. as "pertaining to the people." From late 15c. as "pertaining to public affairs;" meaning "open to all in the community" is from 1540s in English. An Old English adjective in this sense was folclic. Public relations first recorded 1913 (after an isolated use by Thomas Jefferson in 1807).

Public office "position held by a public official" is from 1821; public service is from 1570s; public interest from 1670s. Public-spirited is from 1670s. Public enemy is attested from 1756. Public sector attested from 1949.

Public school is from 1570s, originally, in Britain, a grammar school endowed for the benefit of the public, but most have evolved into boarding-schools for the well-to-do. The main modern meaning in U.S., "school (usually free) provided at public expense and run by local authorities," is attested from 1640s. For public house, see pub.
public (n.) Look up public at Dictionary.com
"the community," 1610s, from public (adj.); meaning "people in general" is from 1660s. In public "in public view, publicly" is attested from c.1500.