Add egg to your hamburger?

I went to this cookout once and had the best hamburgers ever. When I asked what was in them I was told egg. I think there was also pepper. Does anyone know how you make a hamburger with an egg? Does this really make the hamburger taste good. I bought a can of salmon once, and followed the directions to make salmon burgers by adding and egg. They were delicious. My kids even loved them. I wonder if you just cook the hamburgers the same way. What else should I add to the hamburger, other than egg and pepper ... if this works?