Every domain must be registered or reserved so that the rest of the world knows who is using that domain.  In order to register a domain, you have to pay someone to register it for you.  Domains are registered for anywhere from 1 to 10 years, in 1 year increments.  If you register a domain, then let the registration run out, without re-registering or renewing, the domains soon becomes expired.

Expired domains are domains which someone else registered and used at one time, but no longer use today.  Some resources have suggested that purchasing expired domains and forwarding them to existing sites is a good way to get traffic.  Unfortunately most search engines are getting better and better with detect these methods of trying to boost traffic, so if this method works well now, it may not work nearly as well in a month or two.  Whatever the case, there are most likely some links out there to many expired domains and if you can find enough links and your content is close to what the previous content of that domain was, you may be able to profit from purchasing an expired domain.  Most registrars do not make distinctions between domains that have never been registered and those that expired more than month ago.