Fire Emblem Fates is split into 3 story paths. Conquest is one of the 2 base stories, the other being Birthright. The other story path can be bought digitally at a discount through the in-game store. The 3rd story path is Revelation, a DLC that was released later. 
You need to be have completed chapter 6 in either game to access the other stories, and the DLCs, path. 

Conquest is the hardest of the 3 paths having no ability to grind experience from maps, tougher mission objectives, and giving less money and experience for those missions.