Widgets are little chunks of information that can be moved around to any location on a WordPress site that’s “widgetized”. Usually a theme will have at least a widgetized sidebar. Some will add widget areas to the header or footer, and in the case of theme frameworks, much or all of the site will be widget-friendly.
The standard widgets are things like category listings, archives, a list of pages, recent posts, a search bar, links, etc. Many plugins will add additional plugin options. A particularly useful widget is the text box, in which you can add all kinds of useful information or even javascript code.
The widgets page is one of the easiest areas of the admin panel to manipulate, because widgets can be dragged and dropped to any widgetized area.
Note that there are two areas with available widgets: Available widgets and Inactive widgets. All widgets start off as “available”. Once you’ve used one, if you decide to delete it, you can drag it into the “inactive” area and the content/settings will be preserved in case you might want to use it later.
The inactive area also saves widget content if you switch themes, because you will need to reset your widget options.
Helpful hint: if your theme is widget-friendly, by default the theme will fill the sidebar with content such as the blogroll. Assuming you don’t want the default content, you will need to move at least one widget into a widgetized area to override the default options. If you don’t want any sidebar content, the best option would be to drag an empty text box into the sidebar.