This means taking everything that one is entitled to - whether reasonable or not. It comes from Shakespeare's The Merchant of Venice, in which Shylock insists that the merchant, Antonio, should give to him a pound of flesh even if he dies in the process.
The clever payoff at the end of The Merchant Of Venice reveals that although Shylock can take his 'pound of flesh', he is not entitled to one drop of Antonio's blood, and since it's impossible to extract one without the other, the Merchant lives on.