Learn Turkish: Demek ki yurt dışına gitme arzun sadece küçük bir hevesti. - It means your desire to go abroad was just a small passing fancy.

This is the core of this lesson! When linking an unfulfilled or abstract action to an abstract noun like arzu (desire), fikir (idea), or şans (chance), we use the short verbal noun suffix -mA to create a noun compound. It forms the base gitme arzusu (the desire of going). To make it 'your desire', the 3rd person compound suffix -su is replaced by your 2nd person possessive suffix -n, resulting in gitme arzun.

What does 'Demek ki' add to the sentence? Could I just use 'Demek'?

While demek on its own means 'that means' or 'meaning', the addition of ki makes it a conjunction used to express a sudden realization or a conclusion drawn from evidence. Demek ki translates nicely to 'So it turns out that...' or 'It implies that...' and carries a stronger sense of realization than just demek.

Why is 'yurt dışına' in the dative case? Doesn't the verbal noun 'gitme' change how cases work?

No, verbal nouns act just like regular verbs when it comes to the objects and directional cases they demand. Because you go to a destination (bir yere gitmek), the verbal noun gitme still requires the dative case on the destination. Since yurt dışı (abroad) is already a compound noun, it takes the buffer letter -n- before the dative -a, becoming yurt dışına.