XXX: Native speakers with Donald Duck expertise please help with the terminology :-)
The most important feature of DNS is that it is a huge distributed database that is organized as a hierarchy of domains. Every object in the DNS is identified by a domain name, which is basically a sequence of labels, separated dots. For instance, the name moneybin.mcduck.com is in the mcduck.com domain, which in turn is a subdomain of com. An IP address can be attached to a domain name by creating a so-called A (for address) record that associates the name (moneybin.mcduck.com) with an IP address (e.g. 10.8.7.6). Anyone can then look up the IP address for moneybin.mcduck.com by querying the DNS for all A records associated with that name.
Likewise, the DNS can be used to find the domain name associated with an IP address as well. This is called a reverse lookup, and works like this: first, the IP address (say, 10.8.7.6) is mapped to the domain name 6.7.8.10.in-addr.arpa. This is just the numeric address read backwards with a in-addr.arpa tacked onto it. Then, the DNS is queried for PTR (a.k.a. pointer) records associated with this name. If everything is set up correctly, the query should return the name moneybin.mcduck.com. This approach looks somewhat complicated, but I hope it will become clearer in a second when we talk about delegation.
Usually, adminstration of the data within a domain is delegated to the owner of that domain. In sticking with our example, there would be a domain administrator at McDuck, Inc. who is running a DNS server for the mcduck.com domain. He'll create A records for scrooge (Scrooge's personal workstation), moneybin (the machine that controls access to the vault where Scrooge keeps all his gold coins), and goldcam (a little webcam that lets Scrooge look at all his money even when travelling).
Now if someone asks the DNS for any records associated with moneybin.mcduck.com, the DNS delegation mechanism will redirect him to the DNS server at mcduck.com, which gives him the authoritative answer that moneybin's IP address is 10.8.7.6.
Where things get really interesting (from a security perspective) is that parts of the in-addr.arpa name space are delegated just like the ``normal'' name space. If a company has been assigned the IP address block 10.8.7.*, they are also given control over the 6.7.10.in-addr.arpa domain so they can go and maintain all the PTR records themselves rather than bothering their ISP all the time.