Google displays a special ad if your query includes the site: operator, followed by a domain name: "Do you own domain.com? Get indexing and ranking data from Google."
Many webmasters use the site: operator to check the number of pages indexed by Google, so it's a good opportunity to promote Google Webmaster Tools.
This isn't a regular AdWords ad, since it's labeled as "Google promotion". From what I know, it's not even possible to create an AdWords campaign for all the searches that use the site: operator.
In a Scoreboard of Words, a Cultural Guide
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