I believe what that means is that the tree is private so others can not look at it. However it is searchable in that it turns up in search results and then if you want to look at the tree itself you have to message the tree owner and ask them for access.
EDIT: This is what Ancestry says
Private Tree
This setting makes your tree "Private" so that it can't be viewed as a Public Member Tree. Note that the information from your tree will still be indexed for searching, but those who find your information can't view your tree without your permission.
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 the Connection Service on Ancestry sites 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.
(Option) Also prevent your tree from being found in the search index.
Note: although your tree will instantly become public or private, it usually takes about a month or more to be reflected in the search index.