Contingent capital is debt that converts into equity when there is a crisis or when certain triggers are met. 
Regulators have made no secret of their fondness for contingent capital - it keeps down the cost of capital in the short term, by classifying it as debt, but provides a buffer in case of emergencies that can be switched into loss-absorbing equity.
Although most contingent capital will be debt that converts, in extreme circumstances, into equity, i.e., so called contingent convertible bonds or Cocos. There are other kinds of contingent capital, e.g., the equity that the Royal Bank of Scotland can raise from the government in times of stress. In that case there's nothing underpinning that in the form of debt, it is just a kind of promise.