What is ‘Buß-und Bettag’ and why is it a public holiday in only one German state?

What is ‘Buß-und Bettag’ and why is it a public holiday in only one German state?

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The German state of Saxony has a public holiday this Wednesday for Buß-und Bettag or Day of Prayer and Repentance. What is it and why does no other state mark it in the same way?