Probably a short form of Silvanus. This is the name of a companion of Saint Paul in the New Testament. Paul refers to him as Silvanus in his epistles, though it is possible that Silas was in fact a Greek form of the Hebrew name Saul (via Aramaic).
As an English name it was not used until after the Protestant Reformation. It was utilized by George Eliot for the title character in her novel 'Silas Marner' (1861).