This is the best card ever printed. Every guardian who has ever run Prepared for the Worst on Stick to the Plan should immediately understand the significance of a side deck that can be stacked with weapons.
In a normal deck, you would hard mulligan for a weapon and forgo most economy cards, but with Underworld Market you can safely mulligan however you want. Let's say you choose to run 6 illicit weapons in a rogue deck, which could include any of (Chicago Typewriter,
Beretta M1918 , Colt Vest Pocket, .41 Derringer, Switchblade, etc.). If you put all of them into your market deck and 0 into your main deck, the odds that you do not see a weapon in the first two turns are:
(4/10)x(3/9)x(2/8)x(1/7)x100% = 0.48%
In other words, without focusing on mulliganing at all you can reliably draw a weapon within the first two turns 99.5% of the time. Going a step further, if you choose to make 100% of your illicit deck cards weapons, you can guarantee a weapon draw in your opening hand.
Separately, combo decks that might work off of cards like Fence or Pickpocketing can now reliably be drawn within the first five turns of the game. This is incredible given that the Rogue class struggles a lot with card draw. Effectively you can run a deck that does not have to worry about its starting hand and can now solely mulligan for economy cards like Faustian Bargain, 21 or Bust, or...whatever the other Rogue cards are.
All of this is nice, but what takes this card from nice to incredible is the fact that both abilities on this card are reaction triggers, meaning that you do not have two reveal the top cards of your illicit deck if you don't want to. Let's say you know what the top two cards are and don't want to reveal them since it would change the order of cards in the illicit deck, well, since this is a reaction trigger, you can simply choose not to.
All in all, this card means that you can effectively guarantee that your primary card type is drawn (weapon, utility, Colt Vest Pocket, etc), while simultaneously allowing you to stack your deck in favor of important cards.