The problem with the CNAME DNS Records in your screenhsot is that you forgot the dots at the end of the fully qualified domain names, which is required in DNS (at least when BIND or MyDNS is used). Examples:
cname pop3.dcs-online.nl mail.dcs-online.nl
correct and equal are these records:
cname pop3 mail
cname pop3.dcs-online.nl. mail.dcs-online.nl.
cname pop3 mail.dcs-online.nl.
what is the purpose of the dns zone?
A DNS zone is a domain for that your DNS Server is authoritive for. In your example. a dns zone is dcs-online.nl while e.g. howtoforge.com is a different dns zone. So why is it called a zone and not simply domain, the reason is that a zone represents a pert of the dns tree that someone is authoritive for. For example the registry where you registered your domain has just one zone, their zone is "nl" and from their view, dcs-online is a subdomain of their "nl" zone. But to make it easier for everyone to manage dns records, it is possible to delegate a part of a zone to another dns server, in this case, dcs-online.de is delagetaed to your server which enables you to add subdomains and records that are inside the dcs-online.nl zone.
So if I set up (for example) a web-shop that uses SSL for its paying method, I have to use a second ip and than I have to create a second dns zone.