From Diablo Wiki
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 (on each server) are listed forever.
The conquests system went live with the first Season, which was enabled in Patch 2.1, after weeks of testing on the PTR.
Conquests are generally more challenging to complete than a standard Achievement and, as a result, they come with a special perk. If you’re one of the first 1,000 players to complete a Conquest, your name will be immortalized on the Conquest Leaderboard for the rest of the Season. These slots are first come, first served, so be prepared to hit the ground running if you want that place at the top of the charts! Conquests will also remain rewarding throughout the Season and, even if you don’t place on a Leaderboard, you’ll still earn points toward your Seasonal achievement point total by completing Conquests.
The first official details came in Blizzard's Patch 2.1 preview.
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.