Stasis refers to a complete cessation of movement within an area.
If used when referring to lifeforms, it is also known as suspended animation and denotes the limiting of bodily functions, inducing a prolonged sleep, in order to slow down the the aging process. Most often this is accomplished through cryogenic suspension.
Individuals put into stasis are usually placed in a stasis unit, and can result in being successfully suspended for hundreds of years while being less susceptive to environmental hazards. (TNG: "The Emissary", "Face of the Enemy"; VOY: "The 37's", "One"; ENT: "Precious Cargo) Pre-warp civilizations therefore sometimes use sleeper ships equipped with stasis technology for long-range transport of personnel, usually as colony vessels. (TOS: "Space Seed"; TNG: "Face of the Enemy")
Croden, placed his daughter, Yareth, in stasis in the 2360s. (DS9: Vortex)
Another known application of stasis is to prevent a changeling from altering its form, by use of a quantum stasis field. (DS9: "The Die is Cast")
In a starships sickbay the morgue is equipped with stasis fields to preserve dead bodies until they can be buried or until postmortem is performed.