A widget lives on your homescreen, for example a clock, a weather widget or a power control widget. You can't open a widget if you don't have it on the homescreen (the equivalent of you desktop on a PC) A widget is sometimes a shortcut to an app, allowing you to control it from the homescreen, or see the info without actually opening the app. As for a task manager, Android is actually pretty good about managing memory and tasks. The system will close apps and delegate the memory to apps you are using as needed. This article explains better than I can.
http://androidspin.com/2010/05/25/wh...-with-android/