There are 12 heroes that you can unlock. First you have to discover them through visiting tribal villages, influencing city-states, or completing the heroic tales project in a city. Then you can claim the hero by recruiting them in a city with a monument - this is another city project. Heroes have some pretty powerful bonuses and abilities, so they definitely have an impact on the game. Here's the list of 12 heroes:
Hunahpu & Xbalanque
At this point I'm not sure if future content packs will introduce additional heroes needed for this achievement, but I will update if that ever is the case.