The phrase, "The Union is Dissolved" comes from a South Carolina pamphlet announcing South Carolina's repeal of the Constitution and succession from the United States.
It references the concept of a UNITED States of America, which is often referred to as a Union of States.
With So. Carolina leaving the Union in the form of succession, the Union was dissolved. Other states would follow suit.
Since South Carolina was one of the original colonies, it was especially dramatic that one of the original 13 would leave the Union.