Most of us use an email service on the web, such as Gmail, Outlook, or Yahoo Mail. That means that our email messages are stored on their servers in the cloud, and typically isn't ever downloaded to your local system. There are some ways you can do this, however, to keep your own copy of those valuable email messages.
First, check for a download option that may be provided to you by the email service itself. It may let you download a copy of your messages directly to your computer.