The Text
New States may be admitted by the Congress into this Union; but no new State shall be formed or erected within the Jurisdiction of any other State; nor any State be formed by the Junction of two or more States, or Parts of States, without the Consent of the Legislatures of the States concerned as well as of the Congress.
The Congress shall have Power to dispose of and make all needful Rules and Regulations respecting the Territory or other Property belonging to the United States; and nothing in this Constitution shall be so construed as to Prejudice any Claims of the United States, or of any particular State.
The Meaning
Congress can admit new states into the Union, but a single state cannot create a new state within its boundaries. For example, the state of New York cannot make New York City a separate state. In addition, two states, or parts of states (i.e. Oregon and Idaho or Wilmington, Delaware, and Philadelphia, Pennsylvania) cannot become states without the consent of the various state legislatures and Congress. Although an original version of the Constitution included a requirement that each new state join the Union on equal footing with the other states, the language was removed before the document was approved. Nevertheless, Congress has always granted new states rights equal to those of existing states.
Not all of the lands that are owned or controlled by the United States are states. Some lands are territories, and Congress has the power to sell off or regulate the territories. This includes allowing U.S. territories to become independent nations, as was done with the Philippines, or regulating the affairs of current U.S. territories like the District of Columbia, Guam, or Puerto Rico. In addition, this provision gives Congress the power to set rules for lands owned by the United States, such as the national parks and national forests. The last sentence of this clause makes sure that nothing in the Constitution would harm the rights of either the federal government or the states in disputes over property.