What is Handoff?

Handoff lets you start something on one Apple device and continue on another — begin an email on your iPhone and the draft appears in your Mac's Dock, ready to finish.

It requires the same Apple ID, Bluetooth and Wi-Fi on both devices, and the switch at Settings → General → AirPlay & Handoff. The Universal Clipboard (copy on one device, paste on another) is part of the same feature.