This should be done after final formatting and layout because this is the stage that checks all the little details. Does a chapter end with a single word on its own page? Has a photograph separated from its caption? Are the chapter numbers in correct sequence? Are the fonts consistent throughout? Is the table of contents complete and correct?
While everyone else along the way will probably have found spelling mistakes and grammatical errors, this is the stage when the document is checked word by word and sentence by sentence. Proofreading involves looking specifically for all those typos, spelling mistakes, misplaced punctuation, grammatical errors, wrongly numbered sections, unevenly spaced lines, uncaptioned photographs; the list goes on. Without this stage, however well you have written and edited, your work may come across as unprofessional.
The extent to which you need any of these stages depends on the purpose of your written work. An informal letter or a menu on a blackboard doesn't need to be perfect. But if you have invested a substantial amount of time in writing, and are about to spend a substantial sum of money on printing or publishing, you should certainly have your work edited and proofread. Who will believe your business plan if you can't even spell? Who will enjoy your story when they can't follow what is happening? Who will understand your user's manual when they can't understand the sentences it contains?
