The Cryo-prison is where criminals (apparently mostly or all mutants) are imprisoned after being shrunken and frozen in the cylindrical Reanimator. (Which should probably be called a Deanimator when performing this function.) It is staffed by heavily-armed guards in protective armor.
The structure on the top of the tower in the exterior view is the prison ship that Ransik steals and takes to 2001 by means of a time hole after taking over the prison and apparently killing Alex.
In Reinforcements From the Future pt. I this prison was identified as the Funaro Maximum Security Prison, named after well-known fan Chris Funaro.