I would describe it as earthy, spicy, pungent, flowery and warm. Comparing it to other kinds of ginger it kind of smells like a cross between turmeric and ginseng.
While Calgon's Hawaiian Ginger is somewhat light and citrus-y, it is also very pungent. It smells like Hawaii, and very common among 13-year-old girls, though it's a little more sophisticated.