Under "Settings" -> "Users & permissions" -> "Permissions" -> "Collections" and "Media" you can set whether a permissions group may delete their own media and edit or even delete other user's media and collections.
Every uploaded file and every collection has an assigned (pixx.io) owner. This is the user who is responsible for its creation (collection) or for the upload (file).
Own media/collections are therefore media/collections that have been created by a particular user. This specific user can have more rights when handling his own collections and media, compared to working with collections/media of others (created/uploaded by other users).