Spoiler warning: Plot and/or ending details follow.
Memory World refers to the final arc in both the Yu-Gi-Oh! Duel Monsters anime and the Yu-Gi-Oh! manga, the latter of which was subtitled Yu-Gi-Oh! Millennium World by Viz. The original manga did not have this subtitle, and the final arc of the manga was comprised of Volumes 32-36. The translated manga follows the first arc, Yu-Gi-Oh! and the second, Yu-Gi-Oh! Duelist (which comprises Volumes 8-31, and includes both Duelist Kingdom and Battle City). The animation, in both its original and dubbed/subtitled forms is the fifth arc, following the first Duelist Kingdom arc, the Rebecca Hopkins and Virtual World RPG mini-arc, Battle City, the Enter the Shadow Realm Virtual World mini-arc, and the Waking the Dragons (the Orichalchos/Doma saga) arc.
Memory World can also refer to the actual place in Pharaoh Atem or Dark Yuugi's memories that Yuugi, Jounouchi, Anzu, and Honda travel to. In the anime, Seto Kaiba also travels to the Memory World, though not by choice.