To summarise:

Every 4 years we add a day to the year, making it a leap year.

Without this the seasons would slip by one day through the calendar every four years.

Every century we miss out a leap year, in order to correct the smaller error in the other direction created by leap years.

Every 4 centuries we still have the leap year at the turn of the century, in order to correct the even smaller error back in the original direction created by missing out a leap year every century. We call this a leap century.

There was one in 1600 (Or should have been). there was also one in 2000.

I have no doubt a further correction will be needed eventually, possibly by missing out a leap century in the year 12000, assuming that the corrections have to alternate by a factor of 4 then 25.

But then again, by then we may be able to steer the Earth and will have gone over to a decimal calendar :-)