A counter claim is a claim that a party to a law suit brings in response to a claim brought against them.

There are rules that require certain types of counter claims to brought in a law suit. If you don't initiate a counter claim in a suit you may loose your right to bring that claim in the future. But, you don't need to worry about that right now. You will have to worry about these compulsory counter claims in your civil procedure class your first year.

Here, the plaintiff lover is suing the doctor over a contract. The doctor is counter claiming for the amount of money she has already paid to the defendant.