Can someone on my network access my Aperture app and how do I prevent it?
You can see them because they have file sharing or some other service turned on. Unless you have turned on some sharing options (like file sharing, remote login, Remote Management, etc…) they can't see your computer on the network. If you have turned on some sharing options then they can see your computer, but probably can't access anything outside of your "/Users//Public" folder on it.