NS Records identify the DNS servers responsible (authoritative) for a Zone. A Zone should contain one NS Record for each of its own DNS servers (primary and secondary). This mostly is used for Zone Transfer purposes (notify). These NS Records have the same name as the Zone in which they are located.
The most important function of the NS Record is Delegation. Delegation implies that part of a domain is delegated to other DNS servers.
You can also delegate sub-domains of your own domain name (such as subdomain.yourdomainname.com) to other DNS servers. An NS Record identifies the name of a DNS server, not the IP Address. Because of this, it is important that an A Record for the referenced DNS server exists otherwise there may not be any way to find that DNS server and communicate with it.
If an NS Record delegates a sub-domain (subdomain.yourdomainname.com)to a DNS Server with a name in that sub-domain (ns1.subdomain.yourdomainname.com), an A Record for that server(ns1.subdomain.yourdomainname.com) must exist in the Parent Zone (yourdomainname.com). This A Record is referred to as a Glue Record, because it doesn't really belong in the Parent Zone, but is necessary to locate the DNS Server for the delegated sub-domain.