The site is run by a W3C Community Group which was initially started by major search engine vendors.
Webmasters can add Schema.org markup (i.e., instances of Schema.org entities with actual properties provided) to the HTML of their website.
For example, the website listing job offers could include Schema.org “JobPosting” markup.
Web crawlers, such as the ones of major search engines, can then process and present this data in a meaningful way. So called rich result snippets, displaying search engine results are often fueled by this kind of data. In the case of JobPosting, regular job search engines will typically also crawl this data and automatically add the offerings into their database.
According to Schema.org itself, more than 10 million websites serve structured data based on the Schema.org vocabulary. As an example, this includes many major news outlets, such as the New York Times (Example page source; search for “ld+json”).
Schema.org for Email is applying the idea of Schema.org for Websites to email content. See Schema.org for Email for more details.