It means "this is how often this periodical is published"
Genghis KHAN published a weekly edition on how to dry out your sword.
It was astonishingly dull.
morning edition ★☆☆☆☆ 朝 (morning) + 刊 (edition) = 朝刊 (morning edition)
monthly ★☆☆☆☆ 月 (moon) + 刊 (edition) = 月刊 (monthly)
evening edition ★☆☆☆☆ 夕 (evening) + 刊 (edition) = 夕刊 (evening edition)