I can speak with my eyes. But this often happens among my intimate friends. I think the reason doesn't lie in whether your eyes can speak or not, but they can understand what you haven't told them because you are too familiar with each other.
Stephen Hawking can speak with his eyes. He can use his eyes to select words in a computer system. But this computer system has been preprogrammed with words and phrases that he often uses. If you mean talk in that way, you can buy such kind of computers. But I am just joking. Seriously, I know you don't need that kind of machines because you can talk.
My mum knows all the suggestions of my body language. Sometimes, I can talk with her by eyes. But I think that's because we have lived in the same house for a long time and we often talk with each other. So we know each other very well. She knows exactly what I want to say and what I am confused about. You can develop this kind of ability by telling with other people so that they can know you better and guess what you want to say.
I think sometimes, if a person says that your eyes can speak, it means that your eyes are beautiful and you are lovely. The people just show their likes in this way. But if you want to make other people understand what you want to say, you may need to communicate with them and tell your true feelings about person or things then they can know your worldview and values. So they know your likes and dislikes well. Then they can guess what you will say.