A "vacation response" (also known as "out of office response" or "away message") is an automatic message that is generated by the mail server in response to incoming messages. It is used to inform people who are sending you emails that you are not available.
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Thunderbird has no simple way to communicate to the mail server that the server should issue vacation responses. There is a protocol for this, but unfortunately it has not been adopted by the majority of mail providers, and as they are generally focused on web mail, there is little likelihood of much change.
One suggestion that is often made is to create a Message Filter and respond to all incoming messages with a template. This solution requires that your device is turned on and Thunderbird is running the whole time you are away. As this has its own issues with regard to security and safety, it is not recommended.
Use your provider's web interface
Most mail providers provide a web-based email interface that can be used to configure a vacation response, and using that is the simplest solution. Listed below are the vacation response links for some of the common mail providers.
See the AOL on-line help article called: Setup an away message in AOL WebMail.
There is a simple tutorial about the auto-responder on GMX's Facebook page.