I think Danny tried to answer this, but I'll try to explain in a more detailed answer below:
A "state championship" means virtually nothing. It implies that the executive or legislative branch of the state's government has declared through written proclamation "This competition is a state championship." Beyond that written proclaimation it has no weight. The winner of any such competition is not considered to be the actual champion of that state. It's only purpose as far as I know is to help that competition be a qualifier for The Jack or The Royal.
Getting into The Jack is a fairly complicated process with several ways to succeed it. There was a great post about it on the CBBQA forum a few years ago, and I'd recommend you read that because I won't try to enumerate all of the rules, especially since they aren't published. A team who received the rules once posted them on their Blog, but I couldn't find that entry last time I looked.
Essentially you have to win one of four competitions (MIM, HLSRS, ARO, or previous year's Jack) or at least one "Jack qualifier" and then have something else happen such as be the only person from the state to win or get drawn in a lottery system. That's the complicated part that I won't even try to explain because besides being complicated, the rules can change at BF's discretion.
To be a Jack qualifier, one of three conditions must be met by the competition:
Be a first year competition with a State Championship proclaimation and have at least 15 teams.
Be a second year or later competition with a State Championship proclaimation and have at least 25 teams.
Be any year competition and have at least 50 teams, regardless of State Championship status.
I think there's also a requirement that the competition must cook chicken, pork, and beef, and there may be an exhaustive list of sanctioning bodies whose competitions are allowed.
Anyway, that's the basics. Maybe some one else will give more details, or maybe you'll find the CBBQA post I mentioned. In the mean time, enjoy.
dmp