Anything gubernatorial has to go with governors, the same way that anything "presidential" has to do with presidents.
A governor is the elected leader of a state in America, and anything gubernatorial has to do with governors and their governing. There are gubernatorial debates and gubernatorial elections. If elected, the governor has many gubernatorial duties to carry out in the gubernatorial mansion. And if a candidate acts out of line, you could say "That's not very gubernatorial" — meaning they’re not acting like a governor should.