A slightly more in-depth explanation, but still simple:
  1. A domain name is registered with an accredited registrar. Through a process of, essentially, paper shuffling, that domain name-to-nameservers mapping is inserted in the root servers, which are well-known servers that all other internet DNS servers know about because they've been told to. In addition, the name-to-IP mappings for the nameservers referenced is inserted in those root servers as well.
  2. One specific DNS server is the master server for a domain. This is the only place that the real domain mapping information is stored. This name server is usually one of the ones listed at the root servers, but doesn't have to be.
  3. There are also slave servers, which copy their data about the domain (``zone'' in DNS-speak) from the master server via a DNS-specific protocol. They are told what the master server is via configuration, not by reading info from the root servers.
  4. The slave servers get a copy of the zone when they start up. The zone data contains information for how often the slave servers should check to get new information, as well as how often to check if that fails and how long to keep data when they can no longer reach the master server. Since the Internet powers-that-be require at least two nameservers be listed at the root, that means that at least one slave server is one of the official nameservers for the domain. That can lead to the official nameservers being out of sync for a period of time. This is what's usually refered to as ``propagation''.
  5. When your computer makes a request for a DNS name, it usually doesn't do the whole thing itself, but asks a local DNS server to get it for you, which it does by asking one of the root servers and then asking the nameservers it specifies. When it does, it also gets a piece of data, also configured in the master zone info, about how long to cache that information, in case your computer or another computer it serves asks for the same data again, before it should recheck with one of the official servers. This is also part of what's though of as ``propagation''.
  6. In recent years, there has been an addition to DNS so that updates to the master server's zone information can get pushed to its slave servers, rather than waiting for them to ask again. This has reduced propagation times significantly, but it isn't terribly widely deployed because it took a while to address some security issues associated with it. There's also a slightly different DNS addition that allows the master server to tell its slaves that it has new information and to come and get it, rather than it pushing new data to them. This has helped, too, and doesn't have as many security issues, although there are a few.
Hope that helped.
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Bitt Faulk