Leo introduces Bruno as his best friend, who conveniently lives above him in their apartment building. They were old friends in Poland who randomly (amazingly) ran into each other one day in Manhattan. Leo tells us that Bruno tried to commit suicide recently, but Leo found him and took him to the hospital. Bruno is not only Leo's only friend, but really his only external reference point—that he exists, that he's alive.
The problem is that Bruno was killed by the Nazis in 1941. He only exists in Leo's imagination at this point, basically as an imaginary friend (although Leo has convinced himself Bruno is alive and well and real).