"We will go to the Mediterranean Sea for summer vacation."
Translation:Yaz tatilinde Akdeniz'e gideceğiz.
It is the combination of two suffixes. First you add the words
yaz/summer + tatil/vacation = "yaz tatili" / "summer vacation"
The -I ending on the second of a pair of nouns makes a compound noun in which the first acts like an adjective to describe the second. English can do this just by putting the two nouns next to each other ("summer vacation") but Turkish uses the little -I suffix to link them.
Then you want to add -DE to say that you are going "in"/"for" summer vacation. However, in general when you have two suffixes combined on the same word you must separate them with a buffer letter -n-. It is simply a connecting sound, it has no independent grammatical meaning.