A case is the sum collection of testimony and evidence that is presented to support an argument in a lawsuit or controversy in court. If a party has strong evidence that supports its legal claims, it is said to have a strong case. The word case refers to the particular suit or trial in which a party is defending its argument.
The word case is often used synonymously with the word lawsuit. However, case also refers to "a cause of action." If the party does have enough to bring a legal action then it is said to have a case. So, basically the word case can refer to a particular trial or lawsuit or it can refer to the degree to which a party has enough support for legal action.