Widgets are third party applications running on a website. Widgets have increased in popularity with the advent of mobile computing and advances of web browser design. Homepages such as Google IG are totally built from custom widgets either generated by Google or other third parties.
Google provides lots of different widgets with one of their most popular being the custom search widget that allows for a custom search box to be placed on a site which will generated custom search results normally targeted to the website owners site when used to search.