WordPress widgets provide design flexibility by allowing you to customize “sidebar” content. I put sidebar in quotation marks because where — and how many — sidebar sections you have depends upon the design of your WordPress theme. A “sidebar” might actually live as a footer or it might contain two sections or there might be a right-and-left sidebar. It all depends on the theme.
A widget is a “configurable code snippet” that makes it possible to modify function and appearance of a WordPress hosted site without the need to know HTML. Whether you are using self-hosted WordPress or managing a site at WordPress.com, widgets are “discrete blocks of goodness” that are added or deleted using a simple drag-and-drop interface.