What the message looks like
554 5.1.8 Sender address rejected: Domain not found553 5.1.8 Domain of sender address does not exist
What it means
The receiving server checked the domain in the sender's address (the envelope sender, also called the return path) and couldn't find it in DNS. The standard name for this status is "bad sender's system address".
This is about the sender's address, not the recipient's. The recipient's address is fine.
Why servers reject it
If the sender's domain doesn't exist, it can't receive bounces or replies. Mail from domains that don't exist is very often spam or forged, so most mail servers refuse it during the SMTP conversation.
If you're the recipient
There's nothing to change on your side. Let the sender know their emails are being rejected, if you can reach them another way. They need to fix their domain or the address their email system sends from.
If you're the sender
Check the address your mail server or app uses as the envelope sender. It's often set separately from the From address you see, for example in a contact form plugin or a server's default settings. Make sure the domain exists and has valid MX or A records. Addresses like root@localhost or wordpress@server1 are common causes.
If you use addy.io
addy.io rejects these emails with 554 5.1.8 Sender address rejected: Domain not found before they're accepted. You can't fix this from your account. The sender's email provider or server administrator has to correct their DNS. See inbound rejections.