A lack of Earth-current weakened the people of the Lesser Redoubt:
"... and the Earth-Current was weak and powerless to put the joy of life into them; so that they went listlessly; but deemed it not strange, because of so many �ons of usage.
It attracts compass needles:
"But, as ever in that age, it [the compass] did spin if we but stirred the needle, and would stop nowheres with surety; for the flow of the Earth-Current from the "Crack" beneath the Pyramid had a power to affect it away from the North, and to set it wandering."
Large quantities can kill creatures:
"And lo! even as I lookt that last time unto the Pyramid, there brake out a monstrous bursting flame, that did rush downward from the Sealed lower part of the Mighty Pyramid. ... And the Flame made a blast in the Night, and a hotness that did seem to wither me, even where I did be from it. And I perceived that the Humans had truly turned loose the Earth-Current upon the Hounds, that I be saved.
It powers all the Pyramid's machinery:
"And lo! as I drew nigh unto the Great Gateway, the lights of the Pyramid to begin to glow again more strong, and the machinery of the Lifts and the Air Pumps to work, because that now the Earth-Current did grow once more to natural strength. And they to have power now to open the Great Gate, which did be done by great machines."
However, there is more to the Earth-current. Simple electricity does not produce strength and vigor in living things in the way Hodgson describes.
The solution to the mystery of the Earth-current is to be found in nineteenth-century ideas about electricity. From the early days of electricity, it was known that animals' muscles were affected by electricity: Galvani's experiments with frogs proved this.
This was taken by many to show that electricity was closely connected with, or in fact was, some sort of life-force. In Mary Shelley's novel Frankenstein, the monster is brought to life by a bolt of lightning.
Even into the first years of the twentieth century, electricity was used as a medical treatment - not only in those specific cases where modern medicine recognizes its usefulness, but to cure fatigue or malaise by recharging the body, and for a wide variety of ailments.
Arthur Conan Doyle's short story "The Los Amigos Fiasco" is about the first execution by electric chair actually strengthening the victim (because electricity is life).
Perhaps it is related to the Earth's magnetic field, which could theoretically be tapped via induction. The Earth does have a magnetic field generated by the internal layers (sometimes referred to as a "geodynamo"). The continual reference to the Earth-Current affecting compass needles might hint that Hodgson was thinking this; however, any electromagnetic force of sufficient strength will affect compasses.
It also does not seem that the Earth's magnetic field would be powerful enough to run all the pumps, elevators, and other machinery of a habitat the size of the Great Redoubt (and also maintain the Electric Circle and Air-Clog as well, but since we don't have such technology, there's no way to know how much power it would consume). The Redoubt may have amazing energy saving devices (it theoretically can draw on millions of years of technology), but there are still limits.
Possibly the Redoubt does draw energy from the magnetic field, but since it's not enough, there must be another energy source. It's probably geothermal.
The Redoubt sits in a valley 100 miles deep, and is surrounded by various geothermal and volcanic features (the Vale of Red Fire, the fire-holes, and probably the Giants' Kilns as well). Farther off, there is an entire Country of Seas and Volcanoes. Geothermal energy should be very abundant.
The Redoubt's power plants probably convert this heat to electricity, and the people of the Redoubt just don't distinguish between the sources of electricity -- they're both from the Earth, after all.
Therefore, this is one of the many seemingly mystical or fantastic elements of The Night Land that actually makes some scientific sense, especially given the science of the time.