Blog "widgets" are extra features or functions that you can add on to your blog. Some of them may be created by the blogging platform (such as blogger) but many of them are created by third part providers. Think of them like cell phone apps.
Usually there is a button in your blog's layout area that says "add widgets." This button will give you basic suggestions recommended to you by the blogging platform company. You can also search for widgets online. The site you find them on will usually have directions on how to install the widget on your blog. Be warned that not all of these third party widgets will be high quality. So shop around.
Some examples of things widgets can do:
-Ways for people to follow your blog (follow by email, follow using Google reader, etc.)
-Follow by Twitter button
-"Like" a page on Facebook button
-Display how many views your blog has received
-Your most popular posts
-Search your blog
There are hundreds if not thousands of widgets. Those were just a few. Widgets are usually placed in your blog sidebars but they can also be placed in the blog footer. Remember, widgets should enhance your blog, not distract from it. Some widgets are fun but before you install it think about how that widget will help your readers.