Litigation is what goes on in court; it is the name for the process of suing someone or trying them for a crime. When families fight over their inheritance, the assets they want may end up being tied up for decades in litigation.
If you paid a man to repair your roof and he never finished the job, and he ignores your calls, the best option is to bring litigation against him: take him to court! We can use litigation to talk about one court case, or about cases in general. When the Congress debates health care, they try to find ways to reduce for medical malpractice litigation, which is one of the most expensive aspects of medicine.