There are a lot of changes, but most of them are small and unnoticed, small changes in interface or placement of options. A few things, however, stick out, and I'd like to address a few of them here.
One major change is the App Store. It felt out of date and clunky in IOS4, and wasn't updated in IOS5. It's about time it got an overhaul. I often said it was ironic that the worst app on the iPhone was the Apple App Store where you get the apps from. The new interface is very slick and pleasing to look at, a much better design. Apps scroll right to left like a book rather than up and down like the old version. There is more detail shown on the search screens making it easier to determine what might be a good app, and the app detail screen now shows what has changed in the newest version and a version history, which was a big missing hole in the old version.The screen shots are now at the top of the detail page, which gives a good visual, but means more scrolling to look at the description which is my main interest. Not really a flaw there, just a change that is better for some and worse for others. The only down side I've found is they failed to correct one thing I disliked in the old version. When you're scrolling through apps and go to the detail of one, then press back, it still goes to the beginning of the list you're scrolling through. When you're a ways into the list, this is a big problem, one I hope they fix at some point, preferably sooner than later. There are times I stop looking at apps because of it. This could mean lost sales, purely do to not saving a page state.
The main change I have noticed in the Mail App is VIP contacts. You can set in a contact for it to be VIP. What this means is that there's a new item on the Mailboxes page called VIP. In it, you will find all conversations from all accounts where one of the senders is a VIP. Very helpful when you get as many emails a day as I do.
The big change here is the changes to the Photo Stream and iCloud. Apple added the ability to have multiple streams, and to share those streams. It still has the default Photo Stream that everything is automatically added to, though it's now on an Photo Stream tab in the Album view instead of listed as an album, but now you can have more than one stream. You can create a stream on the Photo Stream tab, or when you are adding photos to it. You add them, not by clicking Add To, but clicking Share and choosing Photo Stream. In other apps, when you go to select a photo, it no longer shows all albums, just those with pictures in them. Empty albums are hidden now. Below your albums, other apps show your photo streams, and you can select pictures in them the same way you do in regular albums. The only thing you can't do is edit them in the Photos App. On the computer now, Photo Stream now shows up as a drive in Windows with all the streams there. You can create streams there and add photos to them. You can also share photo streams, except the default, with other people, both in the Photo App and from the computer. It sends them an invite and they can accept and it adds the stream to their account, if they have an Apple ID, or gives them access via the web if they don't. The stream is read only for them, and they show as subscribers from your end. You can also make a stream public, which makes it available to anyone via a web link.
Do Not Disturb
This is the function I was waiting for, and it's very simple. In the root of the Settings App, there is now a switch for Do Not Disturb. Switch it and all alerts, sounds, and vibrations are temporarily turned off until you turn Do Not Disturb back off. This means not having to change the settings, then going back in and setting them all back, and means not having to turn the phone off if you want to be sure it won't make a sound, won't vibrate, and won't create light. A very good feature.
A major feature added is Facebook integration. In IOS5, Apple added Twitter integration, allowing sharing to Twitter natively in apps and allowing authentication with Twitter without a separate login in apps. And the ability to have multiple Twitter accounts that you can switch to to share to different ones without logging out and back in, including within the Twitter App itself. I was looking forward to the addition of Facebook integration, hoping it would be the same. And it does, all except the multiple accounts part. That was a part I was hoping for, because I have a Facebook account specifically for some pages I run that I want kept separate from those for my friends and family. It isn't uncommon in this day and age where Facebook is sometimes required for professional or work purposes to separate those aspects from personal friend and family aspects. Facebook integration doesn't allow this. If you use multiple Facebook accounts, you have to log out of one and into the other to share to another Facebook account. However, unlike Twitter, the active Facebook account for IOS isn't the active Facebook account in the Facebook App, so you can change the account in the app without effecting the account in IOS. The other Facebook apps, Facebook Messenger, Facebook Pages, and Facebook Camera, use the Facebook App as the default no login required account to log into and don't connect to the IOS account at this point. I have not had a chance yet to work with the sharing, so can't yet judge on how it works yet.
Podcasts and iTunes U
In the past, the only way to put podcasts and classes from iTunes U onto your IOS device was using iTunes on a computer and syncing them. They appeared within the Music App. With IOS6, these have been separated out. They are no longer present at all within the Music App, but each have their own app. These are installed apps, not built in, so have to be installed from the App Store. They allow management of your podcasts and iTune U classes respectively from in the app on the device. You can purchase or subscribe from in the app, and download them as needed, either manually or automatically, just like songs you purchase from iTunes and songs that you have in iTune Match. You can delete them from the device and redownload them later if you want to. A big improvement.
The rest of the changes I've noticed are cosmetic. Colours have changed in the Camera App. The Music App has been completely reworked in how it looks, with reordering of the default placement of tabs, but no real changes I can see except the removing of podcasts and iTune U classes. There are some small cosmetic changes in the Mail App. The iTunes App has been reworked in the same way the Music App has, so the two match. The Find My Phone App looks a bit different after the update as well. There are supposed to be a lot of enhancements to the Maps App but other than cosmetic changes, I don't see much difference. Maybe I will find more as I use it more.