Here's the story. Thanksgiving always falls on the last Thursday of November, the 24th this year.
Since schools are closed on Thanksgiving Day and the following day (Friday), obviously Saturday & Sunday as well, many families like to go to WDW for the 4 day weekend. It has evolved to become one of the busiest weekends of the year at Disney!!!

There is a very bright side to this though, the absolute slowest time of the year immediately follows this weekend! You will see the crowds drop off dramatically as of Monday, the 28th. That trend will continue into the first 2-3 weeks of December, until the kids are released from school for the Christmas vacation.
Another wonderful benefit that you will have from going at that particular time, is that Christmas decorations will seemingly "magically" appear overnight after Thanksgiving!
As someone advised earlier, stay away from the Magic Kingdom during that peak time. Epcot is always a good choice during those busy days, since it seems to be able to handle huge crowds better than the other parks.
Maybe resort hopping would be a fun activity on the busy days.
I see that you are from Scotland! You MUST check out a show or 2 by Off Kilter when you are at Epcot!

They are an AWESOME Celtic rock band with an award winning bagpiper that has been performing on a stage in front of the Canadian pavilion for 8 years! Be sure to request Scotland The Brave!
You can check the entertainment schedule for Off Kilter's show times.
ENJOY!
