The Stocks widget shows a scrolling ticker of any symbols you've added in the Stocks app, along with their current quote, whether they've gone up or down, and—for companies—their current market capitalization. You can tap and drag on the scrolling stocks, just in case the one you wanted to look at scrolled by too fast. And tapping on the widget will take you to the Stocks app.
Like the other apps in Notification Center, you can place the widgets wherever you like, if you've chosen to organize them manually. (If you organize by time, they'll always be at the top.) However, you can't configure anything else about them, other than turning them off or on.
While I turned the Stocks widget off—I don't need constant reminders of our economic woes—I find the Weather widget extremely handy. I hope that Apple will extend this widget space to further apps and perhaps even third-party developers at some point in the future; I can imagine plenty of apps where I'd want the option to get a quick glance at their status without launching them—a news reader for example, or social networking client, or an app that provides sport scores. Or, for that matter, let third-party makers of weather and stocks apps provide their own widgets, if users would prefer them.
The last part of the notifications overhaul in iOS 5 is the improvement to the lock screen. In previous versions of iOS, if you got multiple notifications while your phone was asleep, they would appear in a blue dialog box along with a brief description: two missed calls, a voicemail, a text, etc. But once you unlocked the phone, those messages would disappear, so it was incumbent on you to remember what they were.
Now, your lock screen gives you a scrollable list of all your notifications, listed in the order that you received them. As with Notification Center and banners, an icon tells you what app the notification is for, along with a short description of the alert. Swiping any icon will unlock the phone and take you right to that application.
Apple has also added granular controls for notifications along with all these new options. In addition to now being able to enable or disable sounds, badges, and alerts, as you could previously, you can now also choose whether an app's notifications show up in Notification Center or on your lock screen. You can also choose to retain the alert-style notification on a per-app basis, if you prefer, and dictate how many recent notifications appear in Notification Center for the app: one, five, or ten. (The iPad also offers the ability to have 20 notifications displayed for an app.)
However, there are some downsides. For example, there's no longer a way to quickly disable all notifications, as in iOS 4. Now, you'll have to go through and disable all the various options for each app one at a time.