The explanation for the Curious Badge says "Asked a well-received question on 5 separate days, and maintained a positive question record"
What is "well-received" and what is a "positive question record"?
Everything is detailed in this meta post on the badges, Asking days badges.
well-received question on X separate days
A well-received question is one that's open, not deleted, and has a score > 0. If you ask at least one well-recieved question in a UTC day and none of your questions that day are deleted, downvoted, or closed, you get one more day of credit toward the badge. Whenever the badge criteria is checked, previous asking days are re-evaluated so that there's an incentive to fix downvoted and/or closed questions. The no-deleted-questions criteria is to prevent people from asking several questions at once and deleting any that aren't upvoted or answered to ask another day. (Though this is a losing strategy in the long run.)