Imagine this: you're going on a long trip to a strange place, and you might not ever be coming back. You can only bring one suitcase. Out of your whole life, one suitcase. What would you fill it with? Some warm clothes? Your valuables? Photos of your family? Practical stuff like cookware? Your music? Phone? Books?
As the Jews are taken away from the ghetto to the extermination camps, they're allowed that one suitcase. They're told to leave those suitcases and other belongings, with instructions that they'll be sent after them at a later date. Everyone takes great pains and care to label their belongings, then leaves them behind… at which point they're just tossed onto a pile to be sorted through. They're not going to need them where they're going.
The soldiers who liberated Auschwitz discovered mountains of suitcases. You can see some of them on display at Auschwitz.
The suitcases and other objects symbolize in a very direct and brutal way just how the Nazis are proceeding to destroy all evidence of Jewish existence and culture. It represents complete displacement. We see photos, letters, jewelry, objects of Jewish ritual… all the things that make up a life. The Nazis just sort them all into piles, either for distribution and sale elsewhere, or just for destruction.
Each suitcase represents a life. Things that matter to people, people who left them behind with the desperate and completely irrational hope that someone will bring them along. When you see workers in the warehouse sorting through all those belongings like so much trash, it's a statement about the utter dehumanization of the people who treasured those things.