It's explained in vague terms, but it's a sort-of green liquid energy of immense power permeating the planet that gives life to everything and feeds on dead organic matter, the idea being that once a being die it returns to the Lifestream and a new being is born in its place. A cycle of reincarnation that governs the Gaya of FFVII.
And it seems it contains the afterlife since in one novel, Aerith' soul travels inside it and meets with the souls of other deceased FFVII characters like Dyne or President Shinra.
Though for my previous comment i was mostly joking, because the Lifestream tends to be very radioactive in its raw form, among other things. Hence why the setting of FFVII has the Shinra corporation treating it like nuclear energy and exploiting it to power up Midgar and other cities.