There are three main reasons to "white out" your members-only pages which all have to do with adding advanced levels of security:
In most cases, your customers will be redirected to a login page instantly when attempting to access one of your members-only pages. However, if your customers has a direct link to one of your members-only pages, it is possible that the customer will be able to view the members-only page for a few seconds before authentication occurs and your customer is redirected to the login prompt. If you don't want visitors to see any information on the page whatsoever, then 'whiting out' the page accomplishes that since the page will be completely white with only a loading icon present until the redirect occurs.
In theory, software developers or those with advanced coding skills could disable the code that authenticates your visitors so that they would be able to prevent the redirection to the login screeen thus allowing those with a direct link to your page and advanced Javascript coding skills to view the page. If you 'whiteout' the page, these developers would only view a white screen and would not be able to view your content.
You likely don't want your members-only pages indexed by search engines like Google which can result in links appearing on Google Searches to your members-only content. The best way to prevent indexing is by 'whiting out' your members only pages. By doing so, Google and other search engines are programmatically told to not index this page so it won't be included in SERPs (Search Engine Results Pages). It is still possible for a search engine to index the page, but it is much less likely, particularly if you white-out your page before ever publishing it since it takes time for search engines to have bots crawl through the internet to index your website pages.
Optionally, you can check the checkbox to help you remember that you have applied the whiteout code to this page, but checking the box is just for your records - you must embed the code into your page to actually whiteout the page.