A music composition by Robert Schumann. It is the seventh piece from the set of thirteen collectively called “Kinderszenen” (English: “Scenes from Childhood”). Träumerei means “to see a dream” in German, and in this case it might be most accurate to translate it as a “dream state of mind.”
It is the tune that Rikudou Reika played after being badgered by Assassin of “Black,” Jack the Ripper. However, Schumann didn’t actually compose this set of music pieces for children, but rather for adults to reminisce and yearn for their childhood—hence the allusion of a tune for the sake of seeing a dream. If Reika knew this, then perhaps she didn’t choose this tune just for Jack, but also to reveal the way she felt as if she were in a dream right now.

Fate/Apocrypha material: Fate/Apocrypha Encylopedia