The casino is where you can take risks to either earn big, or lose your investment. There are 5 types of casinos (after you unlock spin the shank with one of the Jack Of Trades milestones). There is a blackjack table, a find the lady table, a horse racing casino, a slots machine, and lastly spin the shank. I don't really know how to play blackjack, or how the horse betting works, but i can explain the other 3.
In find the lady, all you do is decide how much you want to bet, and choose one of 3 cards on the table. If you win you get 3x the amount invested. But if you lose, you lose all of that invested cash.
In the slots machine its pretty self explanatory if you have ever seen one of these before. You pick how much you want to bet and at the bottom there are your reward amounts.
And lastly spin the shank if basically a Russian Roulette sort of principle. If you can ever find a game, because nobody plays it, you choose how much you would like to spend, then the shank spins, whoever it lands on wins all the money that the players have bet.