Counterparty Risk is the risk that an investor is exposed to when taking out any kind of contractual position (CDS, option, future etc.) The risk is that one (or both) of the parties involved will not be able to meet their obligations. For example, in the run-up to the 2008 financial crash, AIG issued many billions of dollars worth of CDS's on CDOs, and then when the CDO's actually defaulted they could not afford to pay so all the buyers of AIG-issued CDS's would have lost money.
Counterparty Risk is also sometimes known as Default Risk and is a serious problem in the global interlinked financial world. All the different financial institutions have links and ties to other institutions, and an issue at one can have knock on effects to many more and this effect can spiral out of control very quickly.