The phrase "51st state" can be used in a positive sense, meaning that a region or territory is so aligned, supportive, and conducive with the United States, that it is like a U.S. state. It can also be used in a pejorative sense, meaning an area or region is perceived to be under excessive American cultural or military influence or control. In various countries around the world, people who believe their local or national culture has become too Americanized sometimes use the term "51st state" in reference to their own countries. 

Under Article IV, Section Three of the United States Constitution, which outlines the relationship among the states, Congress has the power to admit new states to the union. The states are required to give "full faith and credit" to the acts of each other's legislatures and courts, which is generally held to include the recognition of legal contracts, marriages, and criminal judgments. The states are guaranteed military and civil defense by the federal government, which is also obliged by Article IV, Section Four, to "guarantee to every state in this union a republican form of government".
Who has the ability to actually make one?
Congress has the power to admit new states to the union