In simple words please, what is the "Rendered file" image-format? I've tried to Google the term "Rendered file" "Drupal" to have some clear data about this image-format and what makes it even possible for choosing (I guess, a module I installed for another purpose that does it), but that data I found wasn't clear and didactic enough for me.

My only aim is to use Drupals image API with the monumental module Insert. The display should be "Hidden" for the field (so it would not be duplicated when the image is inserted to the CKeditor). But I ask to know anyway, and that people to come will have a better clearer answer for what is the "Rendered file" format.

Please give the shortest, clearest definition you can, for this term, and in the end, some words about it's connection to the Views module. Thx,
Since Drupal 7 Images can be rendered the same way as any other entity. Images are a special case of a file and file is a fieldable entity.

Fields can be added to the entity and how the fields are displayed can be configured here:

admin/structure/file-types/manage/image/display

But most times you don't want a rendered file, but a resized image. That is provided by the module "image" in core and if enabled you can configure image styles and use this in node displays and views.