Good question. In publishing, proofreading often comes just before the book goes to the printer. This stage is well after the copyediting stage and looks for mistakes the editor might have missed or errors that might have been introduced to the text during the design process. Proofreaders will read the text and correct more minor errors such as incorrect page numbers, misaligned paragraphs, or missing spaces between words.
Copyediting often comes right after the manuscript has been structured and finalized. Copyeditors focus on structure of paragraphs and sentence, subject-verb agreement, readability and accuracy, as well as ensuring style guide adherence. In many cases, copyeditors and proofreaders are not the same person. Having two different people helps to ensure as much accuracy as possible.