Typically when referring to a "subdomain", the requirement is simply to create a record (www, mail, ftp, etc.) within a domain name. Normally an A record.
The true technical definition of a subdomain is the delegatation of a section of name space within a domain to different external name servers than those which are authoritative for the root domain.
"example.com" is a subdomain of "com".
"com" uses one set of name severs for delegation (the .COM TLD name servers).
and "example.com" uses different name servers (DNS Made Easy name servers for instance).
When you notify your registrar to use DNS Made Easy name servers for a domain you have set up in the DNS Made Easy control panel, inside the "com" zonefile new NS records are added/updated for "example.com" that point "example.com" to the DNS Made Easy name servers. That is how domains are delegated to authoritative name servers.
So if you wanted a subdomain for "example.com" (such as "us.example.com" or "europe.example.com") to be managed on other name servers external to DNS Made Easy, then you would create NS records to delegate that part of your domain to different name servers making a subdomain. Then on those name servers there would be configured DNS records to resolve hosts within that subdomain, for instance "www.us.example.com".
How do I delegate a subdomain in DNS Made Easy?