To put it simply, a widget is simply a block that allows you to display information on your website. Widgets allow the user to add information, whether that be images or text, to particular areas of your site.
There are many widgets that are available by default, you may also have some that have been built specifically for you.
To use a widget on a page, look for the "Administer Widgets" button. This will be found in the "Select a template" section on the right hand side of the page in edit mode. If the button is not there or deactivated, this means the active template doesn't support widgets. Clicking the "Administer Widgets" button will bring up a dialog display your available widgets.
Click a widget you would like to use, or simple drag and drop on to the available widgets space on the right hand side. Once you've finished customising the widget click save, and your page will now be updated.