To use Handoff, you must login to iCloud on your Apple computer and iOS device first and have the feature turned on. On Apple computers, this is found under Settings > General. On Apple mobile devices, this is found under Settings > General > Handoff & Suggested Apps.
Handoff may already be on by default. If so, you may have noticed alerts for incoming phone calls on your computer screen or you may have noticed a small icon in the lower left corner of your iPhone (or iPad/iPod) lock screen. This icon indicates that a supported app/program is running on your desktop Apple computer and you can access the same app and whatever file or task you were doing in the identical spot. On the desktop computer, you may notice an additional icon to the left of the Dock.
There are probably many specialized programs on either your computer or iOS mobile device. The Handoff feature only works with selected programs that are on both systems such as Pages, Keynote, Numbers, and the Safari or Chrome browsers (for example).
Below is a video by MacRumors showing how to setup and use Handoff.