The swag is an Australian icon. It's not about your attitude or bravado. It's something to sleep in and on.
It's more than a bedroll. It's a very comfortable, durable and practical mattress wrapped in canvas that you sleep on the ground with.
The name 'swag' derives from when early European pioneers would roll up their belongings in exploration in the Australian outback. These 'swagmen' or 'swaggies' would be able to sleep anywhere on their journey to a new town for work.
The swag used today has evolved a lot since the early days. It's now a pretty heavy item best carried in a vehicle rather than by an individual. It's still highly portable and is carried on the tour vehicles you will travel on or is stored at camps. After use, you roll up and tie the swag in its rolled form for ease of stacking and transportation. It's a relative skill to do this well, as you will experience if you do a trip that uses swags.
The tours that use swags at some stage on their itineraries (not necessarily every night) are classified as Traditional or Bush Camping.
Photos of swags in action:
Swag explanation by guide