A parachute rigger is a person who is trained or licensed to pack, maintain or repair parachute

Parachute

A parachute is a device used to slow the motion of an object through an atmosphere by creating drag, or in the case of ram-air parachutes, aerodynamic lift. Parachutes are usually made out of light, strong cloth, originally silk, now most commonly nylon...

s. A rigger is required to understand fabrics, hardware, webbing, regulations, sewing, packing, and other aspects related to the building, packing, repair, and maintenance of parachutes.
Militaries around the world train their own parachute riggers to support their airborne

Airborne forces

Airborne forces are military units, usually light infantry, set up to be moved by aircraft and 'dropped' into battle. Thus they can be placed behind enemy lines, and have an ability to deploy almost anywhere with little warning...

 or paratrooper

Paratrooper

Paratroopers are soldiers trained in parachuting and generally operate as part of an airborne force.Paratroopers are used for tactical advantage as they can be inserted into the battlefield from the air, thereby allowing them to be positioned in areas not accessible by land...

 forces. These military riggers also pack parachutes for aerial delivery operations, through which military supplies and equipment are delivered by aircraft to combat zones.
Parachute riggers in the Australian Army

Australian Army

The Australian Army is Australia's military land force. It is part of the Australian Defence Force along with the Royal Australian Navy and the Royal Australian Air Force. While the Chief of Defence commands the Australian Defence Force , the Army is commanded by the Chief of Army...

 are responsible for the preparation, maintenance and supply of parachutes and other aerial delivery components.

Prior to commencing the parachute rigger course, all trainees must be static-line parachute qualified.