The government forms a more perfect union by promoting the unification of the states under a single national interest and purpose. This is facilitated by a federal government powerful enough to overrule competitive state interests and, thereby, keep the peace. The notion of forming a more perfect union was a response to the inadequacies of federal government under the Articles of Confederation.
The government maintains a more perfect union through policy that unites the country and encourages both cooperation and interdependence among the states. For instance, eliminating trade barriers between the states, ensuring that states respect contracts, passing laws that are beneficial to the entire nation and providing for national security are actions the federal government takes to promote a more perfect union.
The opposite of the "more perfect union" mentioned in the Constitution would be the disunion that existed during the days of the Articles of Confederation. The national government had insufficient power to make and enforce laws to govern the entire nation and the states acted like independent countries. They instituted policies that antagonized one another, such as placing tariffs on imports from other states. The framers of the Constitution realized that the division and competitiveness among the states was detrimental to the nation's strength.