What is WordPress Blog widget?

WordPress Widgets are WordPress Plugins. After installing a plugin on the WordPress blog, you can active your widget to give more functionality to your blog.
Widgets are usually placed at the sidebar of the blog. They provide a simple and easy-to-use functionality of the blog. Widgets require no code experience or expertise. They can be added, removed, and rearranged on the WordPress Administration Appearance > Widgets panel.

Activate Widgets

To active your WordPress Theme Widget options:

Go to Appearance > Widgets.
Choose a Widget and drag it to the sidebar where you wish it to appear. There might be more than one sidebar option, so begin with the first one. Once in place, WordPress automatically updates the Theme.
Preview the site. You should find that the “default” sidebar elements are now gone and only the new addition is visible.
Return to the Widgets Panel to continue adding Widgets.
To arrange the Widgets within the sidebar or Widget area, click and drag it into place.
To customize the Widget features, click the down arrow in the upper right corner to expand the Widget’s interface.
To save the Widget’s customization, click Save.
To remove the Widget, click Remove or Delete.

There are many plugins , widgets at wordpress.org website to choose from.
Just make sure that when you are installing a plugin, it should be compatible with your version of WordPress blog.

Read more info here: http://wordpress.org/extend/plugins/

References: http://codex.wordpress.org/WordPress_Widgets