Juliek's "last concert" happens just after the prisoners are forced to physically run from Buna to Gliewitz in the snow. This is an example of one of the many "death marches" that took place during the Holocaust. Most prisoners did not survive the march. Those who did, end up in a heap, piling on top of one another for a chance at shelter and possible warmth.
Eliezer, from the pile of men, though he can hardly breathe, notices he is right on top of Juliek, who befriended him earlier in the story. He discovers his father is also nearby. Eventually he makes his way out of the pile of bodies and the next thing he remembers is hearing the sound of Juliek's violin. He falls asleep to this music and when he awakes, Juliek is dead and the violin is smashed.
The significance of this final song could lie in the fact that it was almost a funereal song for the many men who had died and would die that very night, including the musician. It was an ironic and rare moment of beauty and hope in what was otherwise a very desperate and hopeless night. The fact that it sticks out in the narrator's memory also adds to its significance. Consider all the nameless prisoners who Eliezer sees every day. Juliek received a name, and attached to this name was a violin. Obviously something about his playing changed the prisoners' lives for the better. Perhaps Juliek was even a hero for playing music even as he was dying.