This SMTP error message means that the computer which is sending the message is not permitted to send outgoing messages based on the VPOP3 SMTP Service's Access Restrictions.
This is probably because someone is trying to send messages from outside your local network, and you have not configured VPOP3 to allow this. You have to be careful when allowing this, because you may configure VPOP3 to be an open-relay, which is a bad thing.
We have instructions here telling you how to configure VPOP3 to allow relaying of mail from outside your local network.
If you are having this problem for people inside your local network then it may be because someone has changed the default restrictions, or you may have a complex network with multiple subnets defined. In this case, you need to go to Services → SMTP Server → IP Access Restrictions, and check that the required subnets are allowed, or add a new rule to allow the required subnets.
IMPORTANT: Do not add a rule to allow 'any host' to send mail unless you are requiring authentication - see the link above for configuring relaying of mail from outside your local network.
If you are having this problem for people inside your local network, and you believe that their subnet is allowed by the Access Restrictions, then check their email client configuration to make sure that it is using the internal IP address of the VPOP3 server. Some routers have a feature called NAT Reflection which allows you to use the external IP address from inside the network. That is OK, but VPOP3 will see the connection as coming from your network's external IP address, so it will not be trusted. You can either change the email client configuration to use the internal IP address of the VPOP3 server, or add an IP Access Restriction rule to allow just your single external IP address, or set up VPOP3 to allow relaying from external IP addresses.
Note that this is one of the more complex configuration options in VPOP3 because of the risk of configuring it as an open-relay. Unfortunately, we cannot give step-by-step instructions as there are many different possible ways that you need to configure it, so you need some networking experience to decide how you want it configured. If you need help, then we can give help by email to firstname.lastname@example.org, or you can use our paid telephone support service.