Cryogenics was the study of very low temperatures or the production thereof, and the behavior of materials at very low temperature. One was required to contain materials to study inside a Cryogenic chamber in order to achieve low temperatures.
One application of cryogenics was cryostasis, in which lifeforms may age at a much reduced rate or experience hardly any time at all. Cryogenics was sometimes employed by pre-warp civilizations that attempt interstellar travel.
On Earth, in the late 20th century, cryogenics was a completely experimental procedure. Anyone with a seemingly incurable disease decided to get frozen so that in the future, they can be cured. To overcome the needed power source of the current century, the frozen people were placed into a solar satellite. However, it drifted out of the solar system before it was found by the USS Enterprise-D in 2364. Most of the satellite's occupants' capsules were broken and most had died, save for three others. (TNG: "The Neutral Zone")
In the alternate timeline, the cryogenic stasis pods containing Khan Noonien Singh and other Augments were found by Section 31 operatives under Admiral Alexander Marcus and used to create weapons such as torpedoes and the Dreadnought class starship USS Vengeance. The Cryogenic tubes containing Khan's allies were used as blackmail to get him to work for Section 31. After his exposure to radiation, James T. Kirk was placed into Khan's cryostasis tube (found in a torpedo), until Dr. Leonard McCoy was able to heal him using Augment blood. Shortly thereafter, Khan was placed back into cryostasis. (Star Trek Into Darkness)