Like it says in the other comment, these glasses are to be used when belaying so that you don't have to tilt your head up. The lenses are made of a prism-shaped glass that bends the light in such a way that you see what is happening up while looking straight in front of you. They help to avoid neck pain, and they also make it easier to always keep an eye on the climber.
So in theory the glasses are a great idea for people who climb often, or have to belay for a long time, or have problems with their neck. I see a lot of old folks wearing them, so might be especially appealing for older people. I believe the main reason those glasses are not that popular is that they used to be really expensive. I remember them costing around 200 euros a few years ago.
I have also tried belay glasses myself. And while most of my friends who have tried them really liked them, I couldn't stay for longer than a couple of minutes while wearing those glasses myself. Of course, it might be a matter of getting used to the feeling, but I was getting dizzy, and decided it was better for the climber if I took those glasses off.
So my verdict would be that in theory the belay glasses sound like a great idea, and most people seem to like them well enough, but you should try them out yourself before deciding to buy. Even trying them out in the shop could be informative enough.