Having a Hero in your civilization will gain you a massive advantage on the battlefield in the form of attribute bonuses. These bonuses are categorized by two core types (with sub bonuses) as listed below:
Attack bonus: +1% per 5 Hero attacks
Defense bonus: +1% per 5 Hero defense
Provides bonus when deciding winner (ATK / DEF) affects each round & only military units
Unit bonus boost: +1 per 10 Hero influence
Provides unit boost bonus when assigned to army
Resource Production boost: +1% per 5 influence
Provides Resource Production boost when assigned as the Governor-General of a city.