I'm trying to understand DNS a bit better, but I still don't get A and NS records completely.

As far as I understood, the A record tells which IP-address belongs to a (sub) domain, so far it was still clear to me. But as I understood, the NS record tells which nameserver points belongs to a (sub) domain, and that nameserver should tell which IP-address belongs to a (sub) domain. But that was already specified in the A record in the same DNS file. So can someone explain to me what the NS records and nameservers exactly do, because probably I understood something wrong.

edit: As I understand you correctly, a NS record tells you were to find the DNS server with the A record for a certain domain, and the A record tells you which ip-address belongs to a domain. But what is the use of putting an A and an NS record in the same DNS file? If there is already an A record for a certain domain, then why do you need to point to another DNS server, which would probably give you the same information?