State sovereignty is the ability of the state to be independent and have autonomy and control over itself and its decisions. The word sovereign means autonomous, or independent.
In the United States, state sovereignty means that in addition to being members of the “united” states, the country, each state also has its own government. Each state has a legislature that passes state laws, a governor, and a court system. States still have to follow federal laws, but they have the option of making their own laws stricter.
When states make laws that are contrary to those of the federal government, there can be clash. For example, the medical marijuana laws can be considered a states’ right issue, because states want to have the right to make their own laws and not follow the federal law (which outlaws marijuana). These clashes are settled by the federal United States Supreme Court.
When Thomas Jefferson penned the Declaration of Independence, he insisted that "these united colonies are of right, and ought to be, free and INDEPENDENT states".
The same Principle of Sovereignty is involved with the states today, "seperate, but equal", to borrow and twist a phrase.
Even concerning the federal double jeopardy clause of the 5th AM, states are "seperate soveriegns" if they both claim criminal law jurisdiction to a crime, and that is determined to be constitutional.
For example, in my state, Ohio, our state Supreme Court has ruled that OUR Constituion is a "Document of Independent force".
This means total sovereignty. The provisions of any other state constitution are NOT binding on us, as this is true with all individual contitutions.