While the iPhone doesn’t offer the sophisticated widget system of the Android platform, there are three pre-defined widgets available in the Notification Center for weather, stocks, and Facebook/Twitter posting. The Weather and Stocks widgets will display information from the corresponding built-in apps, which you can open with a tap. The “Share Widget” includes options for posting directly to Twitter and Facebook and will only appear if you are signed into either or both of these accounts from the options in your Settings app—note that these have no connection to the individual Facebook and Twitter apps, but are instead tied into the integration built directly into iOS.
You can disable these widgets or change the order of them with a quick trip into the Notifications section in the Settings app. If you’re sorting apps “By Time” the widgets will always appear at the top, but you can re-order them in relation to each other; if you’re sorting manually, you can place them anywhere, even below any active notifications.