Prior to iOS 8, Apple only allowed its native apps like Calendar, Reminders, and Stocks to push data to your Notification Center. To be sure, there were jailbreak tweaks such as NCWeather that would let you add widgets, but that was not sanctioned by Apple and could've nullified your warranty. With the latest iOS, however, Apple has opened up the Notification Center to third party developers and there are already a bunch of apps with widgets available. For example, if you have the Sports Center app, it now has a widget available that you can add to your NC, which will show you updated scores, news, etc.
If you have updated to iOS 8 and want to add a widget to your iPhone's Notification Center, here's how:
1. Make sure you have an updated version of your app that includes iOS 8 widgets.
2. Open your Notification Center by swiping down from the top of your screen.