Evil eyes are monster eyes infected by the chaos. although its weird because you can get EEs from monsters that dont even have eyes,
They are used mainly in BoV/BoE for reputation and for BoE it is also one of the ingridient for their secret liqour. Eyes can also be offered in the place of profession-aquired resources to God of Dead/Goddess/Dragon. They can also be exchanged with tokens or gifts on some monthly and seasonal events
The most common way to get Eyes is to use Rainbow sphere as human to get the rainbow power or the Vertsida plant to obtain rage of vertsida buff for magmar and use these buff in your hunt.
It is possible to obtain EE without using the buff by participating events such as Luck Glow, magic mirrior, heavenly blessing*,Wheel of fortune** . you can also get them from wand* and opening smuggled bags
Currently there is the Evil Eye Pot that you can use within 7min of activation of your RB/RV and it increases the chances of you getting eyes during your hunt. there are also other buffs that increases chance of monsters dropping resources but I do believe it has been discontinued years ago, so the pot is the ONLY way to increase chance of getting eyes
* I have never gotten Eyes from event/items myself but I have heard other people got them before, they may be very rare or discontinued
**You can trade in Tokens you get by playing the wheel of fortune to get Eyes, this is a very nice way to get extra Eyes because all you need to do is do the daily charter quests until enough charters to play the wheel.