How is it that the Winter Solstice can fall on two different days, depending on your location?

The exact time of the Solstice is an astronomical event that occurs at the same precise moment, no matter where you are on the globe. It is the moment when the Sun reaches its most southerly point during the year. This year it occurred at Dec. 22, 00:23 am UT. UT means Greenwich Universal Time. (In other words the United Kingdom Time Zone.) This time translates to 01:23 am on Dec. 22 in Paris, 07:23 pm on Dec. 21 in New York and 04:23 pm on Dec. 21 in Los Angeles.

Since the moment of the Solstice was the evening of December 21st in North America, December 21st is recognized as the date of the Solstice there.

Since the moment of the Solstice was in the early hours of December 22nd in Europe, the Solstice is celebrated on December 22nd there.