Heaviside Layer

The Heaviside Layer is a setting referenced throughout the musical, usually interpreted to be a heaven-like place of rebirth for cats selected by Old Deuteronomy. Despite never physically appearing in the show, it is unknown if it is a metaphysical or otherworldly place within canon.

The purpose of the Jellicle Ball seems to be to invite Old Deuteronomy to where the Jellicle Cats meet, all to ask him to choose one cat to go to the Heaviside layer. In the end, Grizabella ends up being the one sent to the Heaviside Layer, as we see her ascent from either a levitating platform or floating staircase.

Celebration
The Heaviside Layer appears to be something that cats actively want to strive to go to eventually, particularly those of old age. The Jellicle Ball, which revolves around the selection, is described to happen annually, when the "Jellicle Moon" shines bright. Whether Jellicle moon is a special kind of moon, or just the moon for Jellicle cats is unknown.

Theories
There are many theories on what the Heaviside Layer is.
 * The most straightforward interpretation is that the Heaviside Layer is a poetic reference to heaven.
 * The Heaviside Layer is in reality an upper layer of the atmosphere which would have been very well known to T. S. Eliot, who inspired Cats. Oliver Heaviside was a contemporary of Eliot, and at the time, the distant Heaviside layer was evocative to the public because it enabled the first transcontinental radio, and resulted in a Nobel Prize.
 * Andrew Lloyd Webber received unpublished writings from Eliot's widow, saying that cats eventually go "up up up to the Heaviside Layer”. The association of Heaviside with heaven may have appealed to the poet because both words start with "heav". Eliot also referred to the "Heaviside Layer" in his play The Family Reunion which explores the afterlife and heaven.
 * Being sent to the Heaviside Layer is basically being killed, like a ritual sacrifice
 * That the cats in the Junkyard are in something like Purgatory, and the Heaviside layer is real life.
 * When they say to be "reborn into a new Jellicle life", it's true, and the cat will be literally reborn/reincarnated
 * It is theorized that the cats who songs are about, are cats who are putting themselves forward and saying why they should go to the Heaviside layer.

Trivia

 * The Heaviside Layer is an actual layer in the Earth's atmosphere.
 * While the Heaviside Layer is not referenced in T.S. Eliot's Old Possum's Book of Practical Cats, he once wrote to a cohort an (albeit incomplete) suggestion where he proposed that eventually the cats were to go “Up up up past the Russell Hotel, up up up to the Heaviside Layer”.