A tucker bag was originally a crude bag that a swagman would carry his food (tucker) in. It was the Australian equivalent of the American hobo's bag. The traditional tucker bag was essentially what an American would probably call a satchel; a large bag with a shoulder strap, closed with either a flap or a drawstring. (It should be noted, however, that what made a bag a tucker bag was the tucker it contained, and not the shape of the bag).
The second incarnation of the tucker bag was simply any useful carrying bag, usually either a satchel or a fanny pack (a bum bag, in the UK). In the US a certain type of large purse is called a hobo's bag; in Australia these bags may be called a tucker bag, but this isn't very common. The phrase 'tucker bag' just doesn't call high fashion to mind.
More often, the modern tucker bag really is a tucker bag -- a bag for holding food. Modern tucker bags are actually soft-bodied cooler bags, insulated and often with special pockets to hold food, drink, and ice pack. They range in size from lunchbox to picnic basket.