Ts'ui Pen is the great-grandfather of our protagonist, Yu Tsun. He is also, coincidentally, the subject of obsessive study of renowned Sinologist Dr. Stephen Albert. It stands to reason that when the two men get together (apparently by chance), Ts'ui Pen would be the subject of their involved conversation.
Ts'ui Pen was the governor of the Chinese province of Yunnan, a powerful man who gave up his position and all of the prestige that went with it in order to pursue a more scholarly life. As Dr. Albert tells us, he secluded himself in the Pavilion of the Limpid Sun, a kind of summer home surrounded by gardens, in order to build a labyrinth and write a novel. After thirteen years he was assassinated by a stranger. His descendents' confusion upon encountering the mess of papers that were supposed to be his novel, and upon failing to find a physical labyrinth, led them to feel shame at the wasted life of their once-powerful ancestor.
Once again, we're amazed at Borges' skill in packing so much significance into a character who appears in the story as no more than a legacy and a memory. The guy is dead, after all. And yet his persona lingers on not only in the mind of his descendent, Yu Tsun, but also in the body of work that Dr. Stephen Albert takes up as his field of study. Ts'ui Pen's character really does a lot for a dead guy. He's ultimately the source of the theory of time outlined in the story. He also serves to comment on the relevance of ancestry and family honor, the function of literature and scholarship, and the workings of translation and cross-cultural communication. Pretty impressive, huh?