A counterparty is a party with which a transaction is done. If A sells something to B, then B is a counter-party from A's point of view and vice-versa.
The risk that the counterparty will fail to fulfil their obligations - usually either by failing to pay or by failing to deliver securities - is called counterparty risk.
There are a number of ways of controlling counterparty risk. Some are trading mechanisms such as DVP or the use of a central counterparty.
Financial institutions should track and manage counterpart risk in much the same way as any other credit risk, and this should be integrated into institutions' overall risk management system.