You get governor titles from completing specific civics. The first ones are State Workforce and Early Empire. Typically, if I'm not mistaken, there are 2 civics per era that give governor titles. Additionally, you get a governor title when you complete your Government Plaza or a building in it.
You can use a governor title either to unlock a new governor or to give a governor you already have a promotion. I believe that, not counting Future Civic (which gives a governor title every time you complete it) you get 20 governor titles throughout the game, assuming you build a Government Plaza with three buildings. On top of that, you can get three titles from a wonder. That means you get enough titles to basically fully promote three governors or to get all governors with about 2 promotions. So you don't get to upgrade all your governors fully, but you can go for either unlocking them all or upgrading some fully.