"Doubles" references a second, third, fourth, or sometimes 10th copy of a garment for film or theatre. These "doubles" can be created in a costume shop or bought depending on the needs of each show. But, why would a production need a "double" for something? It is slightly different between film and live theatre.
The need for "doubles" in film usually stems form something happening in the filmed scene that would do damage to or change a costume piece. This could be anything from spilling water on oneself to a bloody murder scene. Any time a costume piece could potentially be changed while filming the costume department will ask if a "double" is needed. This way while filming an actor can change out of the "damaged" clothing into a new piece for another take without slowing down filming.
Other reasons for needing "doubles" in film and also theatre sometimes result from a traumatic action such an explosion, war, cake face plant, etc. that would significantly alter a garment in the plot of the production. When this happens, a crafts person would be hired to take an identical costume piece and alter it to the aftermath of the action. This way an actor can change into the damaged or altered costume instead of wading through a bog to get muddy.
A third reason for a "double" would be the need for an identical looking person or stunt double. This time a double would be made or bought for someone standing in for the original actor. You can see this happen in Phantom of the Opera while the Phantom leads Christine down to his lair.
So, anytime you see a character getting soup spilled on them or escaping from the temple of doom, realize there was a costume design team with at least one "double" waiting in the wings for a second take or scene. Sometimes they have a whole wardrobe rack.