This is a common problem when moving a website over from HTTP to HTTPS. In general, the various resources URL's (like images, videos, etc.) that you have in your content and are stored in the database need to be replaced.

This can be done in a number of ways. The easiest would be to use a plugin such as:

This is a very popular plugin that is used to automatically find and replace a specific keyword in your database.

Note: Before doing any changes to your database it's always recommended to create a full backup. 

Once you've installed the plugin the process is straightforward. 

Search for: http://yourdomain.com/
Replace with: https://yourdomain.com/

The plugin also offers a "dry run" option which is great if you want to see the changes before they are applied.