Believe it or not, the military is government, and government isn't always efficient.
"Standby" is a "preparatory command." Usually the order to standby alerts a unit that it will receive some kind of marching orders — "standby to launch."
Unofficially, it's used to tell junior members to be ready and wait. Often, troops find themselves waiting for long periods of time because of logistics or command indecisiveness.
Said sarcastically, "standby to standby" means that a unit is waiting to wait some more.
"Hurry up and wait," also said sarcastically, pokes fun at the military's propensity to perform tasks quickly, and then sit idly for long periods of time.