What does Hannah discover when she returns to the present?

When she returns to the present, Hannah discovers that she has been given the gift of memory or remembrance. Essentially, Hannah was taken back in time to receive an understanding of her Aunt Eva and Grandpa Will's Holocaust experiences. With the gift of remembrance borne of experience, Hannah can now keep the brave legacies of Rivka, Wolfe, Gitl, and Yitzchak alive in the minds of the next generation.
In chapter 19, Hannah is transported back into the present. During an interaction with her aunt, Hannah tells the latter that she finally understands the meaning of the numbers on her arm. For her part, Aunt Eva admits that she and Grandpa Will changed their names after the Holocaust. Eva had been known as Rivka (whom Hannah met when she traveled back in time), and Grandpa Will was Wolfe.
Hannah finally understands that it was Grandpa Will who tended to Fayge's dead body. Grandpa Will had been known as Wolfe then, and he was a Sonderkommando, a slave laborer tasked with disposing the bodies of gassed victims. In the present, Hannah now understands why her Grandpa Will has erratic, frightening outbursts. Her new understanding fuels her compassion for her grandfather and others who suffered during the Holocaust.
So, Hannah discovers that she has been gifted with very important memories when she returns to the present.