Translation:We are going to Greece for the summer holiday.
It's actually a combination of a few things:
The buffer letter -n- is used whenever we have a 3rd person possessive suffix [ -(s)i ] followed by a case ending [in this case: -de ]... even though it starts with a consonant. This is explained (on the right-hand side of the first section) in Tips and Notes about Possessives :-)
"We are going to Greece for the summer holiday"- this only makes sense in English if you are lucky enough to go to Greece for entire 6 week school summer holiday. My 'wrong' answers were "We are going to Greece on our summer holidays" or "We are going to Greece for our summer holiday"