If you are experiencing this issue of images not appearing, then this means the site hosting your images does not support HTTPS.
Here are your options:
1. If you have a small amount of broken images and they are used in a theme, then you can upload the images to the theme directly rather than link them. (Admin > Themes > Theme Manger, click on a theme name > Images tab.)
2. You can check with your image host to see if they offer an SSL certificate (this is what is needed for HTTPS).
3. If your host does not offer SSL you can choose to host your images elsewhere on a site that does support HTTPS.
4. If you are hosting images on your own website and SSL is not offered through the host, you can obtain a free SSL certificate through Cloudflare: