I'm not familiar with this feature of Ancestry, but this is what they have in the FAQ on Personal/Public Member Trees.
Question: What will Ancestry do with my Public Member Tree information?
Marking your Tree as "public" will allow others to see your tree as a Public Member Tree and allows your tree information to be compiled into OneWorldTree.
What does this mean?
By allowing others to see your tree in the Public Member Trees section of Ancestry, you help them discover missing links in their own family trees. Site visitors do not need to be paying subscribers in order to see Public Member Trees on Ancestry.
OneWorldTree essentially merges information from various family trees into one big family tree that can save you a lot of time with your research. By comparing all of the information from many family trees at once, rather than reviewing them one-by-one, you can determine which information is most reliable.
When you allow others to view your family tree information in OneWorldTree, you open the door to finding other Ancestry members who have dates, names and other information missing from your tree. We'll also let you know when we find members conducting similar research, so you can compare notes, ask questions and get answers.
Information about living individuals will never be shown to others without your explicit permission. Additionally, you can choose to remove your tree information from OneWorldTree and your tree from the Public Member Trees section at any time. And remember, just because other members can see your tree information, they still can't make any edits to it. Only you can do that.
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Question: What will Ancestry do with my Personal Member Tree information?
Marking your Tree as "personal" will make your tree "Personal" so that it can't be viewed as a Public Member Tree, and withholds your tree information from being compiled in OneWorldTree.
What does this mean?
Even if you don't share your tree, other members can still learn if a specific deceased individual is in your tree, in addition to the birth year and birthplace of the person and your username (but no personal information about you).
They can then contact you anonymously through Ancestry's Connection Service to request more information. Keep in mind that members who want to learn from your tree may also have helpful information about your tree to offer you in exchange.