To secede is to go your own way, breaking off ties. Usually, this refers to one part of a country that wants to become independent, like the South during the U.S. Civil War.
The Latin word secedere means “go apart” and that's where secede comes from. Don't confuse it with the much more common succeed. Your plan to secede from the state of New Jersey and found a kingdom named Rusty, after your dog, is not likely to succeed.