You do not have permission to send to this recipient

[Owen]

Staff at my office have been getting errors when relaying
emails through Outlook and was wondering if anyone can
help me out.
The errors are:
You do not have permission to send to this recipient:
#5.7.1 smtp;550 5.7.1 Unable to relay for *email*

You do not have permission to send to this recipient:
#5.7.1 smtp;550 5.7.1 *email*... Relaying denied

There was a SMTP communication problem with the
recipient's email server:
#5.5.0 smtp;550 recipient *email* unknown

There was a SMTP communication problem with the
recipient's email server:
#5.5.0 smtp;554 *email*: Recipient address rejected:
Relay access denied

If anyone could tell me what these errors mean, and how
to solve them, it would be most appreciated.

Thanks,
Owen