Search syndication is the process by which search results and mainly PPC search ads from a dominant search engine - Google & Bing - are repurposed on a variety of websites which offer a search box and then search results. Search syndication is use for external and internal search. For some second tier search engines, search syndication is the main source of audience and queries.
These websites are called syndicated search partners and there are different forms of search partners:
toolbars with a searchbox
meta search engines
For main search engines, search partners are a way to extend their audiences and ad revenues. The diffusion of ads on search partner sites is the default setting on AdWords and Microsoft AdCenter PPC platforms.
Ads are triggered by a keyword search on the partner site and served in a similar fashion than on the main search engine. When ads are clicked through, the PPC search engine platform gives the partner a share of the sum paid by the advertiser. For instance, Google pays a 51% revenue share to search partners through "Google on your website". The share is probably higher for big partners.
Google search syndication for internal search on New York Times website:
Syndicated search results at the bottom of an Amazon search result page for "gardening" keyword:
Search syndication traffic has sometimes bad press among PPC advertisers and agencies due to lower click through -bad for quality score - and conversion rates than from original search engine traffic. This is especially true for parked domains traffic. So, some advertisers and agencies opt-out globally from search partners or prevent their ads from appearing on parked domains or other specific locations.