The dried and prepared braids of sweetgrass have been a trade item on the Northern Plains for millennia. We have a great article and video on How to Light a Sweetgrass Braid for Smudging.
This healing herb has a prominent place in daily ritual and prayer as well as a place in aboriginal medicine. The active ingredient in sweetgrass that makes it smell so wholesomely wonderful is coumarin. This compound is a strong anti-coagulant and is used to prevent bloodclots in susceptible persons - used in excess, however, it can damage the liver.
Infusions of sweetgrass were drunk as well as being applied topically for different health reasons. It was even used to treat sick dogs. Interestingly, it was noticed that dogs loved to find patches of sweetgrass and roll around in it and this was used to the advantage of the person seeking the plant, much like pigs were used in Europe to hunt truffles.
The Latin name for sweetgrass is "hierchloe odorata" which translates literally as "sacred grass" and is found both in Europe and America. There are many Northern European traditions associated with it that are similar to the Native American/North American ceremonial usages - for the scent and for use in spirituality and prayer. In North America, it is found across Canada and as far south in America as the state of New Mexico.
Most people burn sage after burning sweetgrass as this will keep less positive forces at bay.