Standby is an action available to a unit. Units performing this action do nothing during their activation, but doing so increases the AP pool available to the union.
A unit will use standby if the union is ordered to stay on their toes. They may also standby if they're activated but don't have an appropriate action. Enemy units may choose to do this if they want to build up for a more powerful attack.
Certain game effects force a unit to standby instead of performing their normal action. On the activation, the reason will be given for failing to perform the action (e.g. insufficient AP), but is otherwise identical to standby.