Have you ever heard of the Holocaust? It was a very sad time in history where many people were killed just because of who they were - many of them were Jewish. Some people use the Holocaust as an analogy when talking about animal rights.
This means that they compare the way animals are treated to the way people were treated during the Holocaust. They say that both animals and Jews were treated unfairly and without respect for their lives.
Just like how during the Holocaust, people were killed for no good reason, animals are killed every day in slaughterhouses just so we can eat them. Some people believe that this is just as wrong as what happened during the Holocaust.
They think that animals should have the right to live without being killed for food, just like how people should have the right to live without being killed just because of who they are.
So, in short, the Holocaust analogy in animal rights is when people compare the way animals are treated to the way Jews were treated during the Holocaust, to show that both are wrong and should not happen.