Each Hero's parameters depend on that Hero's level. Also, you can always check the Hero Card count of any Hero.

You can Level Up your Hero whenever you get the required Hero Card count (which depends on the Rarity of the Hero in question); you will also have to spend some Silver on the upgrade. Level-ups boost Hero's parameters, and the higher the current Hero Level, the more additional Cards and the more Silver you will need to go up yet another level.

You can level up a Hero from their Hero Info, as well as via the Collection menu, by tapping on their portrait.