Apple has removed a lot of old features in iOS 10. The original Lock screen has been redesigned, the Game Center app has been removed and Widgets have been moved. The other casualty of iOS 10 includes the Today view in the Notification Center.
The Notification Center has been redesigned in iOS 10 with a simpler hub for all your recent Notifications, and a search bar for to perform Spotlight Searches. You can find your installed widgets by swiping right on the Lock screen. There is no way to change your Notification Center back once you have installed iOS 10.