"Here’s how it works (note that any time you see “Mac” below, the feature also works on iDevices running iOS 10):
Text or some other item is copied on one Mac. The device then advertises over Bluetooth that it has something in its clipboard, just as it would do if it had content available via Handoff. Unlike Handoff, though, there's no visual indicator on other Macs or iDevices that anything is ready to copy.
Hit paste on the other Mac. There's a pause that accompanies the action—nearly unnoticeable for a snippet of text or a link but long enough to prompt a little progress bar popup for larger images or big chunks of text—during which Mac #2 requests the contents of Mac #1's clipboard, and Mac #1 sends it over.
Though both of your devices need to be signed in to the same iCloud account to trust each other, your data never appears to touch Apple's servers—like Handoff, all communication is local. This also means that Bluetooth and Wi-Fi have to be enabled on both devices, and both devices need to be within range of each other for copying and pasting to work. You won't necessarily need an active Internet connection."