Sharing the Screen of an iOS device
There's no easy way to share a screen from an iOS device on its own, but thanks to a little help from a Mac running OS X Yosemite, there's a way to work around that particular limitation.
Connect your iOS device to your Mac with a Lightning cable, then launch QuickTime Player. Choose New Movie Recording from the File menu, and a window will open, probably showing you the view from your Mac's camera. But if you click the downward-facing triangle to the right of the Record button, you'll have a number of other optionsincluding the name of your iOS device. Choose that instead, and your movie recording window will now show you your iOS device's screen, updating it live as you interact with it.
Combine this trick with the previous Mac screen sharing options, and you'll be able to share your iOS device's screen remotelya great way to help a family member troubleshoot problems on their own iOS device.
Incidentally, if you're looking to view a Macs screen from an iOS device, there are plenty of good apps available, my favorite of which is the iOS version of the aforementioned Screens. Like its desktop counterpart, its easy to use, with plenty of advanced features, and support for the same Screens Connect service.