This case is about the separation of powers between the legislative and the executive branches of the United States federal government. In this case, the Court said that the Senate did not have any power to prevent the president from removing an official from office if the president had the right to appoint that official.
Under the Constitution, the President has the right to appoint many officials. However, the Senate has the right to approve or reject these appointments. In this case, the claim was made that the Senate could make laws that also required the president to get Senatorial approval before he removed officials. In this case, the Supreme Court rejected that claim. They said that the Senate does get to approve or reject appointments, but cannot have any control over whether the president retains officials or gets rid of them.