On examining the first relation, it appears, on one hand, that the Constitution is to be founded on the assent and ratification of the people of America, given by deputies elected for the special purpose; but, on the other, that this assent and ratification is to be given by the people, not as individuals composing one entire nation, but as composing the distinct and independent States to which they respectively belong. It is to be the assent and ratification of the several States, derived from the supreme authority in each State, the authority of the people themselves. The act, therefore, establishing the Constitution, will not be a NATIONAL, but a FEDERAL act.
(James Madison, The Federalist Papers, No. 39)

To explain the term "federal act," the ratification of the Constitution was by not only the individual states but was also by the people of those states. A federal government is formed by a compact between political units (the states and the people of the states in this case) that surrender their individual sovereignty to a central authority but retain limited residuary powers of government.