Widgets are wonderful, fun, addictive little things that can keep you busy for hours. And they can also make your website more interactive and informational for your visitors. Widgets are plug-ins that you put into your sidebar. Some themes are marked "widget-ready" but I've never had any problems using widgets in themes that aren't designated as such. You install widgets just as you would install any plug-in, and then you go to the admin portion of your website, activate the widget (in the plug-in section), then go to the "Design" section and then the "Widgets" tab in that section. There you'll find a list of your installed widgets and an easy interface for adding them and rearranging them in your sidebar(s).
One note of caution: if your site's appearance becomes unaligned or your site isn't showing up at all (heaven forbid!), don't panic. Just go back to Admin and remove the last widget or deactive the last plug-in you installed. Not all widgets and plug-ins are compatible with all themes.