When you move your site to SSL you have to adjust the settings in your Google Webmaster Tools or searches that might still point to your HTTP pages. It’s important to make this change to help keep or improve your Google search rankings and start to point your customers to your HTTPS pages. Google also plans to start flagging sites that have fields to enter a password or credit card information with a red triangle if they currently use for broken HTTP and not HTTPS. Starting in 2018 this will expand to include all websites and will label all HTTP pages as non-secure.
This action could have a dramatic effect on how your website visitors react to your site. Using plugins to redirect traffic to your HTTP pages will also be key to happy and secure user experience. See more articles on securing your website to increase Google ranking.