I just bought a new sleeping bag online and it came in a large draw cord bag and there was also a small stuff sack in the package. What is the point of the large draw cord bag?
It is used to store the sleeping bag, in order to retain the loft. It is not a good idea to store your sleeping bag compressed as small as possible as this will damage the fill. This is very important with down, a little less with synthetic but overall it is crucial to the life of the sleeping bag.
A couple things to remember are you want to ensure the bag is dry before storage and it will be stored in a dry area free of excess condensation. You also want to randomly toss it about in the larger storage bag as opposed to rolling it then storing. Rolling up your new sleeping bag will create creases in the same spot over and over and your bag will develop cold spots where the insulation separates as a result of these creases.
The most ideal storage is fully laid out and hung, however manufacturers provide a breathable bag of what they have deemed is an adequate size to store the sleeping bag in.