A blue bar appeared asking me to reconnect to the internet — what is it?

It means this Mac has been offline for several weeks, and the app needs a brief internet connection to re-check your licence. Nothing is wrong yet — the bar tells you how many days you have, and everything keeps working in the meantime. Just get online for a moment (or click "Reconnect now") and it takes care of itself. Your to-dos and notes stay exactly where they are either way.