The Handoff feature was introduced in iOS 8 allowing you to continue an activity started on one iOS device and continue that activity on another iOS device or on a Mac running OS X Yosemite.
Here’s an in-depth step-by-step tutorial from by Gabriel Theodoropoulos in which you’ll create a simple contacts app that works with Handoff.
The tutorial does a nice job of explaining the handoff feature, the situations you’ll need to tackle for Handoff to work properly, performing a handoff, and in the second part Gabriel gets into continuation streams for communications with the originating app if you need to handle more data than the initial Handoff payload.
You can find the tutorial in two parts over on the Appcoda blog: Part 1, Part 2.
A nice in-depth guide on utilizing the new Handoff feature within an app.