The Constitution means the creation of a general government, stronger than the Articles of Confederation, within the context of a limited representative government.
Not trying to be flippant, it means what it says. We should keep in mind that the several State Delegates came to the convention with the intent to alter the Articles of Confederation to achieve a confederated central government function more attuned to a peace time environment. Some made the point that this would not meet future needs and that a stronger, more fully functional central government was the real need.
Not all found such a proposal attractive. At this time (1787) each State had already written their own individual State Constitution and, as a member of the “Articles of Confederation” was a Free, Independent, and Sovereign Nation State as detailed in:
“Article II. Each State retains its sovereignty, freedom and independence, and every power, jurisdiction and right which is not by this Confederation expressly delegated to the United States in Congress assemble.”
Then too, under the Articles of Confederation the end of the Revolutionary War was negotiated to a final end in Paris with the final result being the “1783 Treaty of Peace” between the United States and Great Britain. In Article One each State is identified and defined as “Free, Independent, and Sovereign.”
Since many (probably the majority) of the individuals of those times viewed themselves as Citizens of their States and not as a country as a whole, it is understandable why a move to a stronger central government would find resistance, even to the point that the State of Rhode Island never sent Delegates to the Convention when it did occur.
Within the Convention it didn’t take long until it became obvious that developing a new central government was in the interests of each of the States and they then addressed the work of defining what was needed. Even so, there were those who were not happy about it and this came to a head in the ratification debates following the ending of the Convention. The definitive source for these debates within the individual States is the five volume set of “Debates on the Adoption of the Federal Constitution.” That they also contain James Madison’s diaries on the Convention itself is a plus.
However, the source most often referenced today are what has come to be called the “Federalist Papers.” Here John Jay, Alexander Hamilton, and James Madison make the case for the Constitution and a much stronger central government. In these three sources the meaning of the proposed Constitution was clearly defined.
Certainly it was to form a “more perfect union.” However, more than a union it was to develop a stronger general’ government for a peace time relationship between the various States. Therefore, the Constitution was first to define that federal government. That definition was based on the concept (accepted among the Founders) that such a general government had not sovereignty or power, or rights of its own, rather, that it existed only within the powers delegated to it by the States. What sovereignty the general government had was limited to that required to enact the powers delegated to it. It was due to this design that Alexander Hamilton argued against the need for a Bill of Rights. Since the federal government was bound to only those delegated powers (as Thomas Jefferson said, bound with the chains of the Constitution) all else was either the States or the people.
By and large what the federal government was meant to due is defined in Article I, Section 8, Clauses 1 through 18 and Section 9 Clauses 1 through 8. These are:
Section 8 – Powers of Congress
The Congress shall have Power To lay and collect Taxes, Duties, Imposts and Excises, to pay the Debts and provide for the common Defence and general Welfare of the United States; but all Duties, Imposts and Excises shall be uniform throughout the United States;
To borrow money on the credit of the United States;
To regulate Commerce with foreign Nations, and among the several States, and with the Indian Tribes;
To establish an uniform Rule of Naturalization, and uniform Laws on the subject of Bankruptcies throughout the United States;
To coin Money, regulate the Value thereof, and of foreign Coin, and fix the Standard of Weights and Measures;
To provide for the Punishment of counterfeiting the Securities and current Coin of the United States;
To establish Post Offices and Post Roads;
To promote the Progress of Science and useful Arts, by securing for limited Times to Authors and Inventors the exclusive Right to their respective Writings and Discoveries;
To constitute Tribunals inferior to the supreme Court;
To define and punish Piracies and Felonies committed on the high Seas, and Offenses against the Law of Nations;
To declare War, grant Letters of Marque and Reprisal, and make Rules concerning Captures on Land and Water;
To raise and support Armies, but no Appropriation of Money to that Use shall be for a longer Term than two Years;
To provide and maintain a Navy;
To make Rules for the Government and Regulation of the land and naval Forces;
To provide for calling forth the Militia to execute the Laws of the Union, suppress Insurrections and repel Invasions;
To provide for organizing, arming, and disciplining the Militia, and for governing such Part of them as may be employed in the Service of the United States, reserving to the States respectively, the Appointment of the Officers, and the Authority of training the Militia according to the discipline prescribed by Congress;
To exercise exclusive Legislation in all Cases whatsoever, over such District (not exceeding ten Miles square) as may, by Cession of particular States, and the acceptance of Congress, become the Seat of the Government of the United States, and to exercise like Authority over all Places purchased by the Consent of the Legislature of the State in which the Same shall be, for the Erection of Forts, Magazines, Arsenals, dock-Yards, and other needful Buildings; And
To make all Laws which shall be necessary and proper for carrying into Execution the foregoing Powers, and all other Powers vested by this Constitution in the Government of the United States, or in any Department or Officer thereof.
Section 9 – Limits on Congress
The Migration or Importation of such Persons as any of the States now existing shall think proper to admit, shall not be prohibited by the Congress prior to the Year one thousand eight hundred and eight, but a tax or duty may be imposed on such Importation, not exceeding ten dollars for each Person.
The privilege of the Writ of Habeas Corpus shall not be suspended, unless when in Cases of Rebellion or Invasion the public Safety may require it.
No Bill of Attainder or ex post facto Law shall be passed.
No capitation, or other direct, Tax shall be laid, unless in Proportion to the Census or Enumeration herein before directed to be taken.
No Tax or Duty shall be laid on Articles exported from any State.
No Preference shall be given by any Regulation of Commerce or Revenue to the Ports of one State over those of another: nor shall Vessels bound to, or from, one State, be obliged to enter, clear, or pay Duties in another.
No Money shall be drawn from the Treasury, but in Consequence of Appropriations made by Law; and a regular Statement and Account of the Receipts and Expenditures of all public Money shall be published from time to time.
No Title of Nobility shall be granted by the United States: And no Person holding any Office of Profit or Trust under them, shall, without the Consent of the Congress, accept of any present, Emolument, Office, or Title, of any kind whatever, from any King, Prince or foreign State.
By 1791 the Bill of Rights was added to complete the initial Constitution, however, these are not like lists of rights in prior documents. In fact they were of two types. The first eight are exclusionary in that they exclude’ the federal government (and only the federal government) from doing specifically defined acts. (Note this has been extended to the States with the 14th Amendment  and the case of Texas v. White .
This meets The Common Law evolution as the primary source of the Constitution in the creation of a general government.