Why having sign-off is important
It's tempting to just ask a client in an email if they're happy with the work you've done in order to move on from one stage of the project to the next, let's say from the script to the storyboard stage for example.
The problem with just asking the client if they're happy is that it's slightly vague. It needs to be more official to keep everyone on the same page.
Having the client actually sign a document to complete a stage makes things much more clear, it's an official act that provides a document you can refer back to should the client wish to make changes to a stage further down the line after it's been signed off.
A sign-off sheet also gives you the chance to highlight all the work you've done for a particular stage, noting down in one place the work you've done helps the client appreciate just what goes into a motion design project.