Old English seolfor, Mercian sylfur "silver; money," from Proto-Germanic *silabur- (source also of Old Saxon silvbar, Old Frisian selover, Old Norse silfr, Middle Dutch silver, Dutch zilver, Old High German silabar, German silber "silver; money," Gothic silubr "silver"), which is of uncertain origin.
It seems to be Germanic/Balto-Slavic (source also of Old Church Slavonic s(u)rebo, Russian serebro, Polish srebro, Lithuanian sidabras "silver"), but has long been presumed to be a Wanderwort (a loan-word that has spread among several languages) displacing the usual IE word for the metal (represented by Latin argentum; see argent).
Basque zilharr "silver" usually is considered a loan-word from West Germanic, but the Germanic form lately has been compared to old Celtic words used in Spain, and because the rest of Celtic uses the argentum word, this suggests the borrowing might be in the other direction, and Germanic word might be from "a Hispano-Celtic innovation due to an Iberian donor language. In this connection, the old comparison of Basque zilharr is attractive" [Boutkan].
As an adjective from late Old English (also silvern). As a color name from late 15c. Of voices, words, etc., from 1520s in reference to the metal's pleasing resonance; silver-tongued is from 1590s. The silver age (1560s) was a phrase used by Greek and Roman poets. Chemical abbreviation Ag is from Latin argentum "silver."