Until the 1930s, almost all films were projected in black and white. The screen itself had some bearing on how they looked.
Silver has a very reflective quality, which helps the light shine back with particular luminosity. Black and white films, which relied heavily on the reflective quality of light, thus benefited from being screened on a silver surface.
Movie palaces in the 1920s began to coat their screens with actual silver or silver-like compounds in order to produce the sharpest and clearest image.
Color films don't need the reflective quality to look their best. Silver screens thus faded as color films became popular, though the term "silver screen" remained.
3D films tend to look very good when shown on a silver screen. The rise in 3D movies in the late 2000s may herald a revival of actual silver screens.