Although national standards vary in detail and quantitatively, and depend on the application (medical, etc.), the basic requirement is that any metal surface that a human can encounter during operation should be connected appropriately to the appropriate PE wire (usually green or green/yellow), which in turn plugs into a good PE "ground" connection at the socket.
Thus, should anything fail inside to apply substantial voltage to the metal surface (such as a capacitor from line to chassis shorting), sufficient current will flow to blow the fuse or circuit breaker, and there shall be only low voltage from the metal surface to "ground" (e.g., water pipes) to avoid a shock to the human.
Double insulation requires that two levels of insulation must fail before such a connection to the metal occurs.