(covers information from several alternate timelines)
The memory center was the section of the brain responsible for memory.
In 2371, a holographic Reginald Barclay told The Doctor that kinoplasmic radiation was affecting the memory centers of his brain, thus preventing him from remembering his "real" life as Doctor Lewis Zimmerman. (VOY: "Projections")
In an alternate 2372, Lieutenant Lasca suggested that Harry Kim could have had his memory centers altered so that he believed his story of being an officer aboard the USS Voyager was true. (VOY: "Non Sequitur")
In 2374, The Doctor detected a high concentration of biogenic amines in Seven of Nine's hippocampus which were blocking portions of her memory center. (VOY: "Retrospect")
Soon after, Chakotay urged Curneth to tell him how the neurolytic emitter affected the memory centers, so as to prevent Kellin from forgetting him. (VOY: "Unforgettable")
In 2377, The Doctor discovered that the memory centers of B'Elanna Torres' brain were radically altered as the result of Kadan's abductions and illegal experiments. (VOY: "Workforce, Part II")