Standby is used to make sure the amplifier is quiet and lower the power dissipation inside the amplifier during times when you will not need it for some period of time. Breaks in song sets are the ideal illustration. If you'll be coming back to the amp within a short period of time (under an hour, say), flip it to standby.

Standby also serves as a softer power up switch. To get the most possible life from a set of tubes, the tube heaters should really be hot before the main power supply is applied to the tubes. When tube rectifiers are used, the rectifiers do this almost automatically. However, when solid state rectifiers are used in an amp, the main power supply comes up almost instantly, and this can shorten tube life by the somewhat-esoteric means of cathode stripping. The standby switch can be used to prevent this.