Definition of to form a more perfect union?

This, I believe comes from the Declaration of Independence. A union is a joining together.

At the time of the declaration, the country was not really a country at all, just a bunch of states that might well have become small countries in their own right, as in Europe. Some states were not really interested in joining at all and some states almost immediately wanted to leave this early "union of states." Some of the southern states still do, and there are plenty of people who would be glad if they did.

But, at the time, the idea of forming a powerful "United States of America" by collecting together a fairly unwilling agglomeration of people (usually, especially in those times, to be able to fight wars more efficiently) was a "shaky union" that would be better if were able to become a "more perfect" union. Like most politics, it's really just flowery rhetorical hyperbole that really means nothing in reality.