From the Super Mario Wiki
Mrs. Gammliss is a neighbor of Mario and Luigi's, who lives in apartment 5C of the building that Mario Brothers Plumbing is located in. Somewhat deranged, Mrs. Gammliss believes that she's an opera singer, when in actuality, her singing is quite poor, to the point where much of it is incomprehensible and capable of shattering glass. Due to her obsession, Mrs. Gammliss almost always sings in place of normal talking.
Little is revealed about Mrs. Gammliss' backstory, except that she becomes notorious towards her neighbors due to her poor attempts at singing. During the events of "Opera", Mrs. Gammliss' voice finds its way down the building's garbage chute and into Mario Brothers Plumbing one morning, waking up Mario and Luigi in the process. Unaware that her singing is bringing much grief to the Mario Bros., Mrs. Gammliss continues and shows no sign of stopping.
Unable to escape from Mrs. Gammliss' voice, Mario, Luigi and even the Ratigator attempt to shield themselves by wearing earmuffs, but are unsuccessful in doing so. Mario eventually calls up to Mrs. Gammliss through the garbage chute, explaining that her singing is driving them crazy. Mrs. Gammliss apologizes, but her voice manages to break a glass that Luigi had been holding in the process.
After Mrs. Gammliss refuses to cooperate after being asked to lower her voice for a second time, Mario decides to fight fire with fire, and accompanied by Luigi, the two of them sing several high notes back up the garbage chute at Mrs. Gammliss. Their singing results in a crashing sound from Mrs. Gammliss' apartment, and she begs them to stop, as their voices are destroying her apartment. Mario agrees that he and Luigi would stop if Mrs. Gammliss would stop as well, and the two parties manage to reach an agreement.