Age in the search engine marketing world, or more specifically the SEO realm is primarily referring to the domain age, page age, content age, user account age and other historical data associated with that URL, in essence, it’s how long your website has been around for.
Google and other search engines may take into account the historical data associated with your domain, therefore using your domain/content age to calculate trust and authority. In some instances, if Google’s looking to show up-to-date content in their search engine that’s relevant to the current trends, it may use the age metric to filter out the old content, and therefore display the newer entries that were recently indexed. I assume they obtain this data via a ‘who is’ search or by when the page was first indexed in their search results.
On the other hand, a lot of SEO’s believe that Google favor sites that have been around longer than others, and therefore rank higher in the search results, but this hasn’t been confirmed. Some ranking factors are proven, some are controversial and are just opinion.