There are many instances in which you have a private event that you want to "publicize". e.g., events in which only a certain member of a subgroup or a member of a club can access the opportunity. However, if the event is only in the subgroup, normally the individual would have to navigate into the subgroup to see the event. With visibility for non-members, people who are NOT members, can search and see the opportunity without even being a member. But for them to register, they would have to request to be a member or login.
There are two types of visibilities:
Search Page - Do you want the visibility of the event to be on the "get involved" page or not?
And lastly, do you want the visibility to be on the group page (in which the event is created for) or not?