Paralysis was a neurological condition in which an individual was unable to move. It could be complete or partial.
In 2368, Lieutenant Worf's spinal cord was crushed by a falling cargo container, causing paralysis. Jean-Luc Picard believed that either he or William T. Riker could learn to live with the disability, but not Worf. (TNG: "Ethics")
The term could also refer to the inability to function efficiently because of a continuous influx of problems to solve. In 2268, when the USS Enterprise and its crew were malfunctioning and fainting under the influence of the space amoeba, James T. Kirk remarked that they seemed to be in the middle of a creeping paralysis. (TOS: "The Immunity Syndrome")