What you are referring to is a block quote. It is often used to show that the text which has been marked is not a creation of the editor but has been taken from a source and used verbatim. These are of great help to explain things in a better way when a question is being answered.
When a question is being asked, there is no necessity for this to be done and therefore no option has been provided for text to be marked as you have described. If you would like to mark anything as a direct quote, you could just enclose it within double quotes and place it as a separate paragraph.
Even if you are not an editor you can provide helpful answers to others on this site. When answering a question, you can mark a direct quote by highlighting it and using the double quote symbol below the text box.