The Black Market is, essentially, where you manage your arsenal, inventory and banking.
You keep track of your Z Credits here, you can earn free Z Credits, you can buy Z Credits and you can convert your credits into supplies or money.
Most weapons are bought with in-game cash that you've earn via dueling and killing zombies. But some weapons (such as The Honey Badger) require credits to buy instead of cash. This can often be rather irritating but these weapons (known as Credit Weapons) deal more damage and have a higher duel score than their same/lower
Each weapon can be from class I to class VI. You can upgrade each of your weapons from class I to VI by using an often inordinate amount of supplies for each; but it is worth it since you get to kill zombies and other players a lot easier this way.
Next you have the equipment sectiion.
The equipment section is where you buy your health packs, energy drinks, stamina pills, lockpicks, and scratch cards under the "Consumables" section.
The "Support' section is where you keep your duel items and defense/boosts, hence it's name.
You use these items for defense and attack, such as Claymore Mines and Hell Marys (the defense is especially important if you're holding a large amount of cash/supplies/both AND don't want to lose it). There are also the Support items, which are usually found upon slaying special holiday zombies, such as the Zombie Mountie or the Zombie Lab Rabbits.
Now you have your Misc. Items... This is where Misc. items that you find during scavenging are put. A more useful thing this section can do is hold Food Bars and Gold Bars, bought and sold to prevent your cash and supplies from being taken from duelers.
Thee misc items are generally just goods you cansell for scrap, but can help when you're ALMOST about to get enough cash to buy that item... Just sell a boot or two.
These misc items tend to be found during normal scavenging...
The misc items that assist in duels and zombie killing you either have to buy or stumble across in a locked room. With the new update you can also hope you get lucky (usually very lucky) when you scavenge the white dots in scavenging.
When Crafting comes out these items will also be useful with crafting various usefull items and weapons.