When you're interested in a woman, compliments about eyes are a charming way to move a conversation beyond trivial topics.
In the first stages of flirting, you don't have much information about her personality or accomplishments.
However, we can all see each other's eyes, and they are an acceptable physical feature to discuss.
If you want to know how to compliment eyes, it requires some forethought.
You must tailor your comment to the woman.
This thoughtfulness communicates that you noticed something specific about her.