…or like this:
Those icons basically mean “hey, I see you’ve got a program open on another device that I can use, too. Wanna pick up where you left off?” If you click that icon, your Mac will, for example, continue an email draft you started on your iPhone. It’s pretty handy if you use it, but if you don’t, those icons popping up and then vanishing can get pretty annoying!
There is a REALLY easy way to stop it from happening, though, and here’s how. Just visit System Preferences > General, and toggle off “Allow Handoff between this Mac and your iCloud devices.”
And that’s all there is to it. You’re done. Finito. You’ll no longer see those icons appear in your Dock. I mean, I think you should at least TRY Handoff if you haven’t, but I ain’t gonna judge you if you get irritated by it.