If you're running iOS 8 on your iPhone or iPad, you've got a new feature called Handoff, which is part of Continuity. The basic premise of Handoff is that you can start something on your iPhone, and pick up right where you left off on your iPad, or even your Mac, or vice versa. The best part is, as long as you've got Bluetooth enabled and your devices are all on the same wifi network, Handoff pretty much just works!
Keep in mind before continuing that you'll need to be using an iOS device that supports Handoff. Currently that lists consists of the following -
iPhone 5 or later
iPad 4 or later
All generations of iPad mini
iPod touch 5th generation
How to access and use Handoff on iPhone and iPad
Ensure both wifi and Bluetooth are turned On across all your compatible devices. For iPhone and iPad, that means you'll need to be running iOS 8 or higher. On the Mac, you'll need OS X Yosemite.
Make sure all devices are on the same wifi network.
Start performing an action in a supported app such as Mail (a complete list is below) on any one of your Handoff compatible devices.
Look at the Lock screen of your iPhone or iPad and you should see a Handoff icon for the app you're using in the bottom left corner.
Swipe up on the icon from your Lock screen to pick up where you left off on the other device. You will need to enter your passcode or use Touch ID if you have them enabled to verify.
Alternately, you can also Double-click your Home button to open the multitasking tray from anywhere. Swipe all the way to the right in order to switch to another device too. Handoff will show up here as well.
That's all there is to it! Anytime you're doing something in an app that's compatible with Handoff, you should see an icon in the lower left of your iPhone or iPad's Home screen that allows you to pick up right where you left off. Currently the following Apple apps support Handoff —
Mail, Safari, Maps, Messages, Reminders, Calendar, Contacts, Pages, Numbers, and Keynote
Developers are also given the opportunity to support Handoff, though it may take some time to see them take full advantage of it. As always, if you've found any really cool apps that make switching devices more convenient than ever, thanks to Handoff, be sure to let me know in the comments!