A standby is something (or someone) you can rely on in an emergency, like the bicycle you keep as a standby in case your old car won't start.
In basketball, the players on the bench are the standbys for their teammates on the court; and in theater, an actor's understudy is her standby. When something is "on standby," it's ready to jump in or be used immediately. And when you fly on standby, you are ready to take an extra seat on a flight if one becomes available. Standby comes from nautical slang for "a vessel kept for emergencies," originally "that which stands by one."