There is no place to save on Mozilla/Thunderbird. Are you really talking about your email providers server instead?

I created a file in Thunderbird for incoming e-mails. That file is now out of date but I want to save the contents of that file somewhere i can if I need to some time in the future use the contents again. How do I do that?

Why do you want to remove this folder from Thunderbird? Email messages are best kept in the email client, IMHO. You can search them, and you can see the ebb and flow of conversation that any message belongs to.

Thunderbird's Archive folders are designed specifically for filing older messages out of sight but close to hand, and in a way whereby they can be searched.

You can remove the old messages to an external storage location, but IMHO you'll need to think carefully about what format you want them in, and how you intend to access or search them. The export systems I have looked at have all been weak when it comes to trying to find something in the exported messages. That's why I use Archive folders in Thunderbird.

https://addons.mozilla.org/en-US/thunderbird/addon/importexporttools/

Thunderbird is email client software running on your computer. If you created the Folder under Local Folders then it is on your computer. If you created it on your providers server then make the local folder and move the messages there.