For example, consider a sample ZoneFile extract for the main name server for a company, example.co.nz, with branches in different cities:
auckland.example.co.nz. ns ns1.auckland.example.co.nz. auckland.example.co.nz. ns sec.my-favourite-isp.co.nz. ns1.auckland.example.co.nz. a 184.108.40.206 hamilton.example.co.nz. a 220.127.116.11 hamilton.example.co.nz. mx 10 mail.my-favourite-isp.co.nz.
In this example, the main name server directly contains the information for the Hamilton branch, but information for the Auckland branch is delegated to another pair of name servers, one presumably maintained by the Auckland branch itself, the other by the company's ISP. The latter is likely (but not guaranteed) to be a SecondaryNameServer, picking up its copy of the configuration automatically from the PrimaryNameServer via ZoneTransfers.
Note the presence of an A record together with the NS records for Auckland. This is needed because the name of one of the name servers being delegated to lies within the domain being delegated. Without this A record, there would be no way to determine the address of the name server without asking the name server itself, which can't be done until you know the name server's address!
Apart from this exemption for A records to break circularity, no other types of records are allowed to be mixed with NS records. Delegation means that all the information for the delegated domain are to be found in the name servers being delegated to.