Senility was a mental deterioration that affected the elderly. Among the more notable victims was Ambassador Sarek just before he died in 2368. (TNG: "Unification I")
In 2369, Els Renora stated to Commander Benjamin Sisko and Ilon Tandro during the trial of the Dax symbiont on Deep Space 9 that she wanted the proceedings to move swiftly and expected to be there until "supper, not senility." (DS9: "Dax")
In the anti-time future, Jean-Luc Picard became inflicted with senility within the 2390s. This impacted his ability to warn others about the anti-time anomaly. (TNG: "All Good Things...")