According to online dictionaries, the definition of this is "the sum of 8 and 1" or 9.
What is the origin of this?
This term originates from the dice game craps. Each round of craps begins with the shooter (the player handling the dice) tossing the dice until either he rolls 2, 3, or 12, in which he case he "craps out," and a new round with a new shooter begins, or he rolls 4, 5, 6, 8, 9, or 10. That number is called "the point," and the shooter tries to roll his point again before he rolls a 7, in which case he "sevens out," and a new shooter takes over.
"Nina" sounds like "Niner" for the number 9, and so became the basis for a number of jocular mantras for a player trying to make 9 as his point. The Random House Historical Dictionary of American Slang lists several of these chants, including "Nina Carolina," "Nina Argentina" (presumably with a long "i" for both words), and "Nina, Nina, Ocean Liner."