WordPress “widgets” provide extra functionality in your site. Normally, widgets are displayed in the sidebar (left or right) or in a footer. Some themes have more than one footer area.
The functionality a widget can provide is varied.
You may include a “text widget” in order to place some text, or embed an image or video in a sidebar or in the footer that appears on each page. You might use a text widget in a page footer to include your name and contact info. This would be displayed on all pages that include this footer area (normally all pages & posts).
A “category widget” would provide a current list of your posting categories, so that a visitor could select a category of posting to view. Normally, a category widget does not display any categories that currently have no postings assigned to them.
There is an “RSS widget” which can be used to pull in postings from another web site, or even from your own site. You set the RSS widget up by including the feed URL and choosing how many articles to include, whether to include just an article title, or to include the title and content of each article, etc.