Besides creating the judicial Branch, “The judicial power of the United States, shall be vested in one Supreme Court”, the Third article of the U.S Constitutions states in its Second Section that “The trial of all crimes, except in cases of impeachment, shall be by jury; and such trial shall be held in the state where the said crimes shall have been committed.”
So the answer to your question is:
The important right of the people that the third article speaks of is: “the trial of all crimes, except those of high treason or impeachment, shall be by jury.
