No idea why, but I have been experiencing the same thing the past couple of weeks on both the MacBook 2013 and Mini 2014… Intermittently I get a message that there is some or other issue with iCloud etc and asks for a password.
I just dismiss the message and it seems to be OK.
If I do react and fill in the password it seems to affect all other devices and I have to sign in on every other iPhone, iPad and Mac…