In publishing after an author is finished revising and all the edits by the publisher have been made, a set of proofs is created. The proofs show how the document will look when printed. At this point someone reads the proofs to catch any missed errors–hence the term proofreading.
You should be in the habit of proofreading all your professional documents, whether emails, memos, proposals, reports, websites, videos, etc. Always read through or look over (or listen or watch) your document to look for those missed errors. Often a simply typo or a mistake in grammar, but sometimes a stylistic error such as missing page numbers or a change in font partway through the document these little errors make your document look sloppy.
Taking the time to proofread is simply being professional in the way you approach your work, including communication.