The tradition is called fukubukuro (foo-koo-boo-koo-roh) and it originates from Japan.
You purchase a bag, contents unknown, from your favorite store(s) and it will contain a variety of products worth 2-3x the amount you paid. For example, a $50 bag at Sephora will contain about $100 worth of products. If the products are gender, color, size, etc. specific, the information will be labeled on the bag so that you don't end up with a bunch of stuff you can't use.
Lucky bags are usually non-refundable and the individual product can't be returned or swapped out for other products.
Beware that some retailers on Oahu stick their unsold Christmas items, clearance junk, etc. into bags and call them fukubukuro bags. These are NOT fukubukuro!!! Fukubukuro bags are supposed to contain current, retail-quality items. Some stores in Japan even manufacture limited edition collector items that are only available in fukubukuro bags. Luckily, most of the Ala Moana stores offer the real deal. But if you see a lucky bag at some random strip mall store, just keep walking.
Fukubukuro is very popular so pick your favorite brand/store, grab your Starbucks, and line up early. If you're going for one of the super popular stores like Gucci, you should arrive by 7am because the bags sell out fast.