Conquests are special Season ladder-only Achievements. There will be around a dozen Conquests each new Season, with leaderboards to show the players who complete them. Blizzard's plan is for each Conquest to be a "first come first served" special where only the first 1000 players to complete it are ranked.
The system is set to debut in Patch 2.1.0, and fans will get to try it out on the PTR before it goes live.
The first official details came in Blizzard's Patch 2.1 preview.[1]
With the start of each Season, players will have the opportunity to earn Conquests. Conquests are special Season-only achievements (offered in addition to the suite of non-Seasonal achievements already available in the game) that represent a variety of challenging goals. These goals can vary in terms of gameplay and difficulty, and some might be easier to complete than others. With tasks ranging from killing Malthael at level 70 on Torment VI to finishing Acts I-V in an hour or less, Conquests are designed to encourage and promote an array of different playstyles.
Conquests are considered “first come, first served,” and the first 1000 individuals to complete a Conquest within a given Season will be immortalized on that Season’s regional Leaderboard. Right now, we’re looking to provide between 10-15 unique Conquests each Season, and each Conquest will have its own Leaderboard. Conquests will also provide achievement points and will count toward your Seasonal point total. These points will be provided regardless of whether your character placed in the regional Leaderboard.