I read about the WordPress "featured image" feature but I didn't understand the benefits of it yet. Does it change the blogs theme layout or is it just used for the blog post layout?
I depends on your theme - they can be used for many things, but generally they are displaying in the list of the post, in the post itself (usually on the top of it). As well they are usually visible when sharing the link (for example in FB).
But however, this is really pretty general question, you would have better to use google first (and maybe looking to the documentation of your theme), for example here: