The Black Market is where you can purcase perks and prison bribes.
A perk gives you a special advantage in a specific area of the game.
To buy a perk, go to the Black Market and ask to see what the dealer has. You will then be presented with some perks and given 10 minutes to decide if you want to buy one before the dealer has to leave. There is an 18 hour wait between purchases, even if you decide not to buy anything from the dealer.
You can view and manage anything you purchase on the Perk Inventory screen.
You can find a list of perks in the game on the Perk Inventory page. Note that not all perks are sold in the Black Market (some are exclusive to the Credit Store).
A Prison Bribe enables you to leave the prison instantly without waiting for the timer to expire or for someone to bust you out.
You can buy up to 10 prison bribes each hour at $10,000 each. Prison Bribes can also be transferred to other gangsters on this tab.