How Oct. 4 - Oct. 15, 1582 came to be simply declared out of existence by Pope Gregory XIII:

The commission sent its report to the pope Sept. 14, 1580. He issued a papal bull on Feb. 24, 1582, declaring that the new calendar would go into force in October (when there were few holy days), and that 10 days would be skipped. The day after Oct. 4 would be called not Oct. 5, but Oct. 15.

via wired.com.

Imagine doing something like that today...