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 cryo-stasis 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.
During the Eugenics Wars, Khan Noonien Singh and his Augments were put in suspended animation through cryogenic means and set adrift in space on the SS Botany Bay. (TOS: "Space Seed"; Star Trek II: The Wrath of Khan; Star Trek Into Darkness)
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)