How is my listing ranked in search?
There is no single position: the order depends on what the traveller searches. First the listings bookable online (payments enabled, calendar up to date or connected), then, within each group, a score recalculated every night and weighed by distance to the place searched.
What moves your listing up: complete photos, amenities and descriptions, an up-to-date calendar (best: connect your Airbnb, Vrbo or Booking calendar in the Calendar tab), fast answers to requests and questions (within 2 hours earns the most), and the contacts and bookings your listing gets.
What moves it down: a request lost over the last 90 days, that is dates your calendar showed as free that you turn down as already taken, or a request left unanswered, and every booking you cancel. Turning down a group or an event never counts against you: only a wrong calendar or silence does.
No host can pay to rank higher.