I would add to Raymond's excellent answer that federal court decisions, particularly those of the Supreme Court, tend to be more permanent than actions by Congress and the President. Congress often checks itself by changing or abolishing laws, and checks the executive branch by cutting or threatening to cut funds. The executive branch can likewise hold up budget negotiations, veto and threaten to veto laws, and can fail to enforce laws or enforce them in ways not intended by Congress. These counteractions can ultimately be nullified by the courts. But nullifying a federal court's decision usually requires a constitutional amendment, only 15 of which have been passed in the last 200 years.
Also having a life-time appointment means that a judge doesn't have to worry about what the public or the the other branches will do to him or her for their decisions. Judges can be impeached, But given that only 6 out of over 1000 federal judges in the last century have been removed from office, the fear of impeachment is pretty remote for the vast majority.