Fame, Hero, and Card levels are dependant upon each other.
Your Fame Level controls your Hero Levels and will open up more areas of Silver City for you in the Cime Map. The best way to earn Fame is to complete Missions.
Heroes gain experience points (XP) from winning Battles. There is a Hero Level cap per Fame Level, so keep this in mind as you use your Heroes. If your Hero has reached their maximum level, you may need to level up your Fame before they can level up again.
Hero Level also controls maximum Card Levels. To increase the strength of a Card, you may need to level up your Hero Level first.
Increasing Hero Level will also increase that Hero’s Health!