Can someone explains what does the above mentioned desk do?
What are their responsibilities and how do they manage them, where do they fit into the rest of the organization?
It is the desk responsible for evaluating scenarios corresponding to the action of counterparties (to existing contracts) failing. Their job is risk assessment and risk mitigation via strategies such as market hedging execution, or new business targeting.
Rather than a "traditional" desk responsible for trading a suite of products (say a bond trading desk trades bonds attempts to ensure that the risk of the portfolio with respect to bond prices is well managed, appropriately sized and positioned favourably) a counterparty risk trading desk manages monetary exposure to counterparties aggregated over many of the sub suites of products, e.g IRS, FXswaps, Equity Swaps, Loans, Cross Currency Swaps, TRS, Options, etc.