Widgets, also known as "sidebar accessories," are a useful tool that allows you to personalize what shows up in your sidebar(s) without having to write any PHP or HTML code. You can add design elements, content, images, gadgets, and more.
If you want to use widgets with your website, you have to be sure you have a widgets-ready theme. Not all themes are capable of using widgets. If you're browsing through themes on WordPress.org, you'll see that some themes have the tag "widgets" or "widgets-ready." You must choose from these themes to be able to use widgets.
Widgets come as a part of your WordPress installation as of WordPress 2.2. For earlier versions of WordPress, widgets were available as a plugin.