Most widgets are associated with an app. When you install an app, the widgets associate with the app will appear in the list of screen objects you can put on your home screen.
There are some apps that are widgets only. For instance, Android Pro Widgets are a collection of widgets. The set of widgets include a calendar widget and a Twitter widget. These widgets are not associated with the various apps, but just accesses them to show information on your home screen. The Android Pro calendar widget can be set up to access your calendar app so it can show your appointments on the widget. If you delete the Android Pro Widgets app, only those widgets will be removed. Your calendar app will still be there as well as your Twitter app.
If you don't use widgets, the existence of widgets on your phone should not really interfere with the operation of your phone.