A drawstring bag or drawstring backpack is a particularly popular piece of tat; one of those items that are useful enough that people will use it, and cheap enough that organizations are happy to put their logo on it and give it away for the free advertising and warm-fuzzies from the consumers.
The standard drawstring bag is a simple polyester fabric bag about 16 inches tall by 12 inches wide with a heavy drawstring that extends out in two wide loops attached to the bottom corners of the bag. These loops, in addition to functioning to draw close the bag, also serve as shoulder loops so the bag can be used as a very light backpack or a shoulder bag.
These bags are generally not so much bags as giant 'pockets'; simply one piece of fabric folded over and sewn up the two sides. They are commonly used as light sports bags, but as they are currently ubiquitous, they get used for all sorts of bag-like uses.
As of the time of my writing this, drawstring bags are basically functioning as the new coffee mug; not only are they useful enough that people will accept more than one of them and cheap enough for any organization to have a few thousand of them printed up on short order, but they are also large enough to hold other promotional tat, most often including pencils, stickers, pamphlets and flyers.