Systemic risk is risk that is posed to the financial system or the economy, as opposed to risk that is faced by an investor or a portfolio.
Systemic risk is most commonly discussed in relation to the risks posed by banks and financial institutions. The failure of a major financial institution can have serious consequences. If a bank fails, not only will its depositors lose money, but it is also likely to renege on obligations to other financial institutions. Both the depositors and the other institutions are then likely to be under financial pressure, which can lead to further failures of both banks and other businesses.
The resulting ripple effect can bring down an economy. Controlling systemic risk is a major concern for regulators, particularly given that consolidation in banking has lead to the creation of some extremely large banks.
Even though governments usually bail out those banks that are "too big to fail", the cost of doing so would have its own effects: not least the encouragement this gives them to be less cautious because they know that they will be bailed out. This creates a problem similar to the conflicts of interest between debt and equity holders. In this case the shareholders of big institutions take the gain if the risk pays off, governments pick up the cost (or part of it) if it goes wrong.