Yes, you must have contributed at least 100 items to the database are can disable ads. From, April 2015:
"To disable the ads, go to your profile then click on your site preferences. In the list of preferences you will see "Disable ads on the site?" and you can choose Yes and then save it. If the option does not appear on the site, then you're not eligible for the feature."
So who is eligible? Simply put, everybody who has contributed at least a hundred different things to the database. That includes images, comments, and databox proposals. If you've been active in the database then you probably have this feature enabled.