In every transaction there is an interaction that happens between more than one party, usually two, a buyer and a seller. The term “counter party” is used to refer to the opposite side in a transaction.
A seller is the counter party to a buyer, and all the like, a buyer is the counter party to a seller. But “counter party” can be used far beyond just finance and trade; in politics democrats are the counter party to republicans and vice-versa. In a more intimate scenario such as marriage, a wife is the counter party to a husband.