I've already covered basic tips and useful hidden features in iOS 7. Now I'd like to cover a few new features that seem important for everyone to be aware of.
Airdrop:
If you've accessed the new Control Panel by swiping up from the bottom of the screen, you may have noticed an icon labeled AirDrop. You can use this feature to share videos, photos, notes, map locations, contacts, and more with other nearby iOS users. Your device automatically sees other AirDrop-enabled devices in the vicinity and uses WiFi for fast transfer of files. The devices use a technology called WiFi Direct, meaning that the they set up a direct network connection between them. There's no need for a wireless router. To enable AirDrop, turn it on in the Control Center by tapping it. You'll be given two options: Contacts Only or Everyone. If you select Contacts Only, AirDrop will only show nearby iOS users if that person is in your contacts. (And apparently uses Bluetooth, not Wifi, to scan for nearby users.) Note that AirDrop only works with the iPhone 5 and later, fourth-generation iPad and iPad mini, and fifth-generation iPad touch. Once you've enabled it, then when you tap the Share icon in an app, you'll see the AirDrop option at the top of the sharing options, and a listing of nearby AirDrop users. You can read a more detailed how-to, with screenshots, on CNET.
Near Me:
Another interesting nearby feature can be found in the App Store app. At the bottom of the screen, it says Near Me. Tap that, and the App Store will show you apps related to your current location, such as an app for a nearby museum or a transit-related app.
Call Blocking:
You can now block unwanted communications from specific people, including calls, text messages, iMessages, and FaceTime calls. You can turn it on for calls and messaging by going to Settings>Messages>Blocked and adding the contact or contacts you wish to block. For FaceTime calls, go to Settings>FaceTime>Blocked.
Stream Your Videos from the Cloud:
If you've purchased movies or TV shows from the iTunes Store, you can now watch those videos by streaming them from the cloud rather than having to download them to your device. You'll see that all your purchased videos are there when you open the Videos app. You simply select a video and then tap the Play button to start it streaming. If you or a friend has an Apple TV, you can stream videos via that device, too, if you install the latest version of the Apple TV software (6.0). On Apple TV, simply go into Settings>AirPlay and select AirPlay from the Cloud. Now when you stream a video via AirPlay, it streams from the cloud rather than your device. It's neat that you can use this feature to watch your videos on a friend's TV if he or she has an Apple TV.
Parallax:
Okay, so this isn't very useful, but it's cool. (Though I have to admit I hadn't noticed the use of parallax in iOS 7 until I read about it.) In the home screen, simply tilt your device slowly back and forth or side to side, and you'll nice that the icons appear to be floating above a static background and to move as you tilt your device. You'll need a fairly finely grained wallpaper in the background in order to notice this effect. You can select a different wallpaper by going to Settings>Wallpaper & Brightness. The effect shows up well against the star-filled sky that I had selected. I like these little touches that Apple adds.