How do I stop 'Google Password Required' pop-up on MacBook Air?

As noted by other users, every day, more than once, I'm getting this message "Google Password Required” on the top right of my screen. The first time I saw it I clicked, entered my password, and was on my way. But the message keeps reappearing, though it doesn’t seem to mind when I ignore it by clicking “x” in the box to close it. Annoying!

[Re-Titled by Moderator]