De is always elided with yeux.
Knowing that, your question is not really about elision but about the difference in meaning between "de + noun" vs "des + noun". You'll find many questions about this on this site, it has been answered before.
As to why it's elided, I would say it's because it's treated as a vowel, so naturally there's an elision. It happens in all words starting with a vowel sound ("d'ici, d'hier, d'avoir"), except those with an aspirated h ("de haricot, de hibou").
It's not that obvious that y is treated as a vowel because technically it's a consonant here. In most other words starting with Y it does acts as a consonant ("lait de yack", "crème de yaourt"). I think the reason is that yeux is a much, much older word and dates from a time when French phonology was very different. Maybe it was pronounced closer to an \i\ sound before it shifted into a \j\ sound.