Featured or Sticky Listings means the listing will be shown at the start of the search, list or category results.  The listing will sort by featured flag FIRST, and then by whatever criteria you define under Directory → Settings → Listings → Sorting.

You can manage the featured listing settings in the plan itself under Directory → Directory Content → Plans. Here is a screenshot of that setting:
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Please note: If you already have listings that have been assigned to a plan and you change the settings, those changes won’t take effect on listings that are already on that plan. However, it will be added to new listings added to the plan in the future.
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​In order to update the old listings, you need to change the plan to something else and save the changes, then change them back to the one with the featured listing attribute.
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You can learn more about plans in this article.