Basically, stuff that is necessary for people to understand who and what you are replying to. If it's a picture, and it isn't directly above your post, you could either reference the picture by saying whose photo it was, or just remove the photo from the quote and replace it with a describing text, such as [photo with glasses and scarf] or something. It makes the page much less crowded, and it is good for those browsing from phones etc.
And yeah, quoting something from the post directly above yours is rarely necessary, unless it is a long post and you are replying to a single sentence or two, then it might be useful.