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:

Army Bonus

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

City Bonus

Resource Production boost: +1% per 5 influence

Provides Resource Production boost when assigned as the Governor-General of a city.