Systemic risk is the amount of risk there is of systemic failure. Systemic Failure as it specifically refers to the banking and financial system means that because some of the banks and financial institutions have become so large that if they were to fail and go bankrupt then the shock that would be sent through the system of their collapse would cause other institutions to collapse.
This situation generally occurs because of the size and mass amount of credit that those failing institutions have both created and are obligated to as it relates to one another. This term very much relates to the "too big to fail" mentality. If banks had to keep full reserves to back up their obligations then the chance of having a system wide failure of all banks would be extremely small, if not impossible. One of the secrets of the Federal Reserve is that in the most recent crises, the system was put at risk because of the vast amount of leverage and credit that the Fed and the banks had created.