It is the night of the Jellicle Ball, the night when all cats gather to learn which among them will be taken from Earth to the Heaviside Layer, there to be reborn as new kitten and have life to live all over again. The cats gather and present an impressive roster of cats that might be the one chosen--the Old Gumbie Cat, Skimbleshanks, The Rum Tum Tugger, usw... In and out of this display, Grizabella slinks along like a hippie who fell out of the Chevy Van and had the snot beat out of her by a gang of bikers. Her story is, she was once a posh feline and has fallen on some VERY rough times.
Now, into this fun and frolic, Rumpleteezer and Mungojerrie, at the behest of McCavity (the mystery cat), kidnap Old Dueteronomy, the cat who will announce the name of the cat destined to be reborn in the Heaviside layer. Why they do this is never explained, and is never the point, for it leads to the pivotal introduction of Mr. Mistoffeles, who has the show's most infectious song.
With Old Dueteronomy released, he announces the name of the cat who will be reborn, and--I bet you guessed this part--it's Grizabella! Once the festivities are over, the show ends with a PSA about the diffenences between cats and dogs.