Lifetime appointments mean that the Supreme Court justices can make their rulings without concern for any political backlash directed against them.
The Executive Branch of government and the Legislative Branch are political in nature, and are subject to the will of the people through elections. The Judicial Branch is intended to provide an independent check and balance on the other branches of government, reviewing whether their actions are in line with the Constitution. Having them serve indefinite terms was intended to keep them non-political and objective in their decisions.
