They're included with some apps, both stock and third party. (Only for iOS 8+, even if an app provides a widget, it won't work on 7.x.x.)
On a device running iOS 8.x.x, pull down the NC and scroll to the bottom if necessary. Touch the bar that says Edit, and all available widgets from apps on that device will be available for you to choose from.
Some widgets are near useless due to poor design (eWeatherHD, at least on the iPad, is a good example). Others are well thought out & incredibly useful, enough so that I've been willing to switch apps or add a new one just for the widget.
As Abazigal mentions though, past a certain point, loading up the NC with widgets becomes less practical, as you'll have to do some scrolling to see them all.