A domain hack is a domain name that blends the text in a web address' domain (before the dot) with its top level domain (after the dot) to create a word (such as youtu.be), or a phrase (such as play.it). These are called "hacks" because they use top level domains in ways that they were not intended to be used. In the example above, YouTube uses .be as part of their link shortening service, even though .be was meant to be used as a country code top level domain (ccTLD) for Belgium. Entercom Communications Corporation does the same thing with their play.it domain name, using Italy's ccTLD.
Matthew Doucette first used the term "domain hack" in a blog post on November 3rd, 2004.