What does the 4 digit number embossed on my LEGO set represent?
That number is not a real number, it is a production code (in your case, 27S5) consisting of 2 digits indicating the week of the year the set was made (in this case, the 27th week), a letter indicating the region the box was made in/for (R = US/Canada, S = Europe, I believe) and the last digit is the last digit of the year the set was made in.

So you have a Gingerbread house made in 2015, in the 27th week of the year (June 29, 2015 - July 5, 2015), and it was produced in/for the European market.

These codes typically go on the seals/stickers closing a box, but in case of smaller boxes that are supposed to be pushed open, the code gets embossed into the package.

And just for comparison - all my Gingerbread houses have production code 31R5 (I'm in the US).

UPDATE 5/2/2016: Here is a list of all the plants referred to by the letter code:

H = Nyíregyháza, Hungary
R = Ciénega de Flores, Mexico
S = Kladno, Czech Republic
Q = Purkersdorf, Austria
B = Shenzhen, China (Not Confirmed)
M = Billund, Denmark (Not Confirmed) 
O = Billund, Denmark (Not Confirmed) 




Note: list attributed to GiliusThunderhead over at the BrickPicker.com forums.