Your event can have three visibility states:
Listed (default) — shown on your profile page, indexed by Google
Unlisted — not shown on your profile, not indexed by Google, people will need the link to find your event
Members Only — shown on your profile page but only guests can register
Updating Event Visibility
You can do this in a couple places.
Events Tab on Your Dashboard
Manage Event Page
Update Your Default Visibility
You can update this on the settings page on your dashboard.