Here are some possible results of states separating from the union:
1) Federal government has less power- If states decided to officially leave the US, they would no longer be under the rules/laws of the United States. Since this is the case, the federal government would have less control over the actions of these various states.
2) Creation of a new country- Just like during the Civil War, if states seceded they could form their own government/country with completely new laws.