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