How to clear the Photos icon badge For some reason that is not clear to me, the Photos app icon on the dock of my Yosemite OS now displays a badge (the number 1 in a red circle top right corner)

First of all, I have no idea what that badge is suppose to represent.  Second, when I launch the app I have not idea what the thing is that I'm suppose to look at, acknowledge or in some way "touch" so that the badge goes away.
If you haven't already, turn on the sidebar - Option-Command-S - then look towards the top and under Shared, click Activity. Likely there is some activity on a shared album or Photo Stream. It may also be someone inviting you to join a shared album or Photo Stream. (I'm not sure how that would show up in Photos, as I haven't had any invitations since Photos was released.)

Either way I'm guessing once you take a look at that area, the badge will disappear.