Essence is a liquid substance containing the vitality of the living thing it came from. When consumed by the Skeksis, it has age-reversing effects, although the lasting properties depend on the race of the victim -- Gelfling essence has a strong effect, while the effects of Podling essence is only temporary.
A being drained of their essence is completely without willpower or energy, and is easy to order about, making a perfect slave, as the Skeksis soon discovered. They also have withered faces and empty, milky eyes.
When SkekTek discovered how to drain essence, the first victims were Gelflings, but after all the Gelflings were exterminated, Podlings were captured and used by the Skeksis.
To drain one's essence, the victim is restrained and forced to stare into the reflected light of the Dark Crystal. Their essence leaves their body and flows through tubes, where it is collected in a vial for later consumption. Only the Emperor is allowed to drink essence, although early in the Skeksis' existence, when drained essence was easier to come upon, all of the Skeksis partook.
Being drained of essence and made into slaves was the ultimate fate of all captured Podlings, and when Kira was captured by the Skeksis, she was going to have her essence drained. However, only a few drops of her essence were collected before the animals in SkekTek's laboratory helped her escape.
In the novelization the Skeksis spoke in their original language (a concept that was ditched in the film) and Essence is known as "Vliya".