In A Civil Action, Cheeseman is a senior partner in a law firm that is representing W. R. Grace, one of the companies involved in polluting the water supply of Woburn, Massachusetts, causing leukemia in children.
Cheeseman is a hot-shot lawyer, one of the best that money can buy. W. R. Grace knows they're in serious trouble and can expect to pay a huge amount in compensation if they're found liable in court. That is why they've secured the services of Cheeseman, as he is best placed to help them avoid liability or, at the very least, reduce the amount of potential compensation as much as possible.
Cheeseman may be a good lawyer, but he doesn't have that much experience at trial. He therefore hits on a strategy of trying to stop the suit in its tracks and prevent it from coming to court. This way, he is sure that he will halt the gathering momentum of the class-action lawsuit against his client.