Elementary Essence — a life-wave that is evolving in a downward direction (in contrast to the human, animal, vegetable, and mineral life-waves, which are evolving in an upward direction). This elemental down-flow, along with the (human, etc.) up-flows, combine to make a complete and uninterupted cycle.
“... we have with us at the present time seven kingdoms in manifestation — the human, the animal, the vegetable, the mineral, and the three elemental kingdoms which precede the mineral.” (Leadbeater, Charles, The Inner Life, paragraph 488 online)

“ ... not only that of humanity and of the animal, vegetable, mineral and elemental kingdoms below it,....” (Leadbeater, Charles, The Inner Life, paragraph 7 online or page 4 hardcopy)

[Life exists in forms that can be described as life-waves. There is] “... a human kingdom, and it is always accompanied by its brothers, an animal, a vegetable and a mineral kingdom. But each of these is steadily evolving; so that the life-wave which is ensouling the animal kingdom of the present day will in the next chain have arrived at the human level and will provide the causal bodies for the humanity of that chain. In the same way the life-wave which ensouls our vegetable kingdom now will ensoul the animal kingdom then, and so on. It of course follows from this that we were the animal kingdom of the [previous chain], and the vegetable kingdom of the chain previous to that.... Consequently the humanity which will commence as primitive man in the fifth chain will not be ourselves at all, but will be the wave next behind us - that which is ensouling our present animal kingdom. In the same way our vegetable monad will have evolved a stage higher, and will ensoul the animal kingdom of that new chain; while the life-wave which is now animating the mineral kingdom will by that time have risen to the level of the vegetable kingdom.” (Leadbeater, Charles, The Inner Life, paragraph 506 online or pages 349-350 hardcopy)
When the present mineral-wave has attained its goal, and has passed to the next higher form of manifestation (the vegetable-wave), a fresh life-wave will follow close behind to take its place. This is the elemental-wave.

The Elemental Essence, as it is called, is evolving in a downward direction (opposite to the human-wave, which is presently evolving in an upward direction). Each elemental-wave will evolve down to the lowest level, then ensoul the mineral world of a future world, and so on, keeping the flow of life waves uninterrupted;
“This Elemental Essence is a phase of the life of the Logos at an earlier stage of manifestation than even the life of the mineral; it is on the 'downward arc' of life, and is 'descending into matter', to become, later, mineral life, and later still, vegetable and animal life.” (First Principles of Theosophy, p. 176)
Click here for an explanation of elemental essence in the appearance of spirit in the uiniverse.

For further reading on the Elemental Essence: