its how many quests you've done. I think it's 4...might be 5.
After that many quests, when you turn in that 4th (or 5th?) quest, you get another quest reward of 2000 dukes and another (nice) reward, and the reward at the top of the trader tab tells you you're advancing quest tier.
The NEXT DAY, the next tier of quests will be available from ALL traders you visit.....rinse and repeat for each tier.
As far as a given day, when your tier is above 1, it seems that you'll get a smattering of quest tier levels available, though i have never seen a day happen WITHOUT getting at least 2 of the top tier (with the exception of tier 5...there is a reward for doing X number of quests when you're already at tier 4, but i've never seen a tier 5 quest)
