Hex Vision was a psionic or similar talent demonstrated by holograms infected with the psychotic hologram psi-virus contracted by Dr. Hildegard Lanstrom, and later Arnold Rimmer and Mr. Flibble. The holo-virus unlocked the dormant, psychic areas of the brain which humans had so far been unable to harness, and enabling hex vision and other abilities. Unfortunately the holo-virus also caused even a genius like Dr. Lanstrom to also go insane.
Hex vision manifested as glowing red eyes, and then beams of an blue electrical discharge or comparable nature, which shot out at the target, covering distances of several metres and causing small explosions when masking contact with a target. The use of said power, although intimidating, was very inaccurate in its aim, even when under the control of a great mind like Dr. Lanstrom.
The ability also severely depleted the hologrammatic lifeform, to the extent that Dr. Lanstrom, though desirous of eliminating the Red Dwarf crew, only employed the ability sparingly. Nevertheless, Dr. Lanstrom did eventually and unwittingly deplete her own life-force through the use of the hex vision, and her form disintegrated whilst giving out one last wail.
Rimmer, by the time he was attempting to fry his shipmates with his hex vision, was apparently too far gone in madness to care about his own survival, or else he believed the ship would sustain him through the power loss. Rimmer was somehow able to use his version of hex vision 'through' Mr. Flibble, a very cross penguin hand puppet which manifested during his mental breakdown.
Rimmer lost the abilities of hex vision when his core program was restored, and all traces of the holo-plague were removed before he could harm the others, or deplete his own life force. This was achieved through a remote link to the Hologram Simulation Suite, which was found by Dave Lister when he was under the influence of Lanstrom's luck virus. ("Quarantine").