Grandfather Arlert was the paternal grandfather of Armin Arlert. After the fall of Wall Maria, he died at the hands of the Titans.
Before the fall of Wall Maria, Armin's grandfather possessed a book containing illegal information about the world beyond the Walls. He gave this book to his grandson, Armin Arlert, who showed it to his best friend Eren, kindling his desire to see the outside world.
During his intimidation, or "rite of passage," from Keith Shadis, Armin states his name and is insulted by the instructor for it. When Shadis asks him if his parents gave him the name, Armin replies that it was given to him by his grandfather.
History: Before the fall of Wall Maria, Armin's grandfather possessed a book containing illegal information about the world beyond the Walls. He gave this book to his grandson, Armin Arlert, who showed it to his best friend Eren, kindling his desire to see the outside world.
How Grandfather Arlert echoes later: During his intimidation, or "rite of passage," from Keith Shadis, Armin states his name and is insulted by the instructor for it. When Shadis asks him if his parents gave him the name, Armin replies that it was given to him by his grandfather. Lamenting over his father's theft of the Founding Titan, Eren names Armin's grandfather among the many lives who could have been saved if his father did not interfere with the Reiss family.
Source: Attack on Titan Wiki, available under CC BY-SA 3.0.