Larry writes about his experience with his fellow guildies and how they bought a capital ship and tried to go for some conquest missions.
Conquests are missions when every week different set of planets are ready to be conquered. Every planet gives different bonuses and every guild can choose where to go and which they can try to "beat". And TOP 10 guilds gets more rewards. So this way it is easier for larger guilds to zerg conquest points and be part of the top 10.
In general conquests are fine and fun but the rewards are not very convenient to the job done. But you can read the whole thoughts on the original Joystiq page.