This statement holds more truth than just some glib little platitude. It's usually used by highly enamoured and romantic people who wish to flatter their equally highly enamoured partner, however there is a far more practical and useful side to this phrase which I will now attempt to unpack for you.
If you've ever been away and slept in a dormitory with other people, you will find that the conversation can sometimes extend quite markedly into the night when the lights are turned off. The same can be equally said for people who will talk for hours on the telephone.
The reason for this is because one of the functions of holding a conversation is to establish attitudes and ideas. We receive all sorts of signals from people and a great many of them come from those 27 muscles immediately surrounding people's eyes. Some of the most subtle motor control in the whole human body is contained in those few square inches and it appears as though we are trained at a very early age to read those signals.
The practical point of this is that without those signals, at least on one front people are more open and ready to speak. By being forced to listen to the little quivers in people's voices and other things like tone and timbre, other world's of information are suddenly opened up. In fact it is often handy (provided you don't fall asleep) if listening to a lecture to close your eyes and actively listen to the speaker.
There is however a very real and sinister downside and that is seen especially in two places: the theatre of war and on the road. Without those signals, there is a reduction (and in absolute terms) of humanity of other people. Soldiers who now operate tanks and planes and missiles can do so in full unawareness of the people they have been ordered to destroy - they just become statistics and numbers. Likewise on the road, because we tend to see cars as objects, we forget that there are people inside those objects.
The next time you go for a drive (or bomb the crap out of an unspecting population) try looking into the eyes of those people and suddenly they will turn into people again, not just numbers and metal objects. On the road it's fun to just realise that behind the wheel of all those other cars are people as bored and impatient as you are.