Widgets are small scripts or applets that can be built into your blog, giving it extra functionality. You can add them to your blog through the "Layout" tab. This will show you a mockup of your blog's layout. In various sections, you'll have the option to "add a gadget." "Gadget" is Google's term for its own in-house widgets. They have plenty of very useful ones, including gadgets that will let readers translate your blog into other languages, display recent posts from Twitter feeds, show your most popular posts, and create a slideshow of photos.
You can also add third party widgets. The "add a gadget" dialog has an "Add your own" option, which allows you to input the URL of any custom widget designed for use with Blogger.