My understanding of Christmas Day is that it was traditionally celebrated on the 25th of December, but when the 25th of December is has varied as calendars changed. Did this mean that when the Julian and Gregorian calenders were used in Europe, that one part of the Holy Roman Empire was celebrating Christmas one week and if you made your way to another part you'd find people celebrating then?
If so, why didn't the 25th of december move to the 15th as all of Europe moved over to the Gregorian Calendar?
The whole point of removing days from the Gregorian calendar was to restore the holidays (particularly Easter, but everything else as well) to the times of year in which they occurred when they were first instituted, in the first century AD.
Did this mean that when the Julian and Gregorian calenders were used in Europe, that one part of the Holy Roman Empire was celebrating Christmas one week and if you made your way to another part you'd find people celebrating then?
Absolutely! And you'd find the same thing with Easter, and with all other festivals. In fact, you'll still find that if you go to Eastern Orthodox churches, which mostly still use the Julian Calendar for all religious purposes. (A few of them have changed to a "Revised Julian Calendar," which's going to be identical to the Gregorian for the next couple centuries. But, most haven't.)
About the only thing that did sometimes change in the Julian-Gregorian transition was birthdays. For example, George Washington was born on a day which was then known as February 11th in the British Empire (which still held to the Julian calendar). However, when the Gregorian Calendar was adopted in 1752, he started commemorating his birthday on February 22nd (which was the Gregorian date of the same day.)