"bill, placard, thing posted," 1838, from post (v.1). Poster boy/girl/child "someone given prominence in certain causes" is attested by 1990, in reference to fund-raising drives for charities associated with disability, featuring child sufferers, a feature since 1930s.
Earlier it meant "one who travels post" (c. 1600); "a post-horse" (1797). Sense of "one who posts bills" is by 1864.
Old English fyllan "to fill, make full, fill up, replenish, satisfy; complete, fulfill," from Proto-Germanic *fulljanan "to fill" (source also of Old Saxon fulljan, Old Norse fylla, Old Frisian fella, Dutch vullen, German füllen, Gothic fulljan "to fill, make full"), a derivative of adjective *fullaz "full" (see full (adj.)). Related: Filled.
To fill the bill (1882) originally was U.S. theatrical slang, in reference to a star of such magnitude his or her name would be the only one on a show's poster. To fill out "write in required matter" is recorded from 1880.