Thursday went to bed and woke up on Friday the 15th. Ten dates in between that nobody lived through — the 5th to the 14th of October 1582, gone, in Spain, Portugal, Poland and most of Italy.
Here's the bit the clerks got right: the weekdays never broke. Thursday to Friday, straight through the hole. The whole point was to lose days off the count without losing the week itself. (Easter was the reason. The spring equinox had drifted about ten days off where the Council of Nicaea left it in 325.)
Which left everyone arguing about rent. If you owed a month, did you owe the ten days you hadn't had? Mostly it got settled by charging pro rata, saints' days shunted along with the rest. The printed decree calls it CALENDARIVM GREGORIANVM PERPETVVM — perpetual. It's out by a day somewhere around the year 4900.
The arithmetic underneath it is that the year runs about 365.2422 days, and Julian assumed a flat quarter. That extra sliver adds up to roughly three days every four centuries, so ten days by 1582 is just the drift catching up. Dropping three leap years per 400 is what makes it hold.
Britain waited until 1752, by which point the gap had grown to eleven days, and the arguing in between was mostly about whether taking a Pope's calendar meant taking his authority with it. The Orthodox churches largely kept the old reckoning, which is why Easter still falls where it does in much of the East.