The psycho Cyan bug in Final Fantasy VI is the combination of two bugs involving the Bushido technique Sky. The first bug allows Cyan or Gogo to counter any physical attack dealt by any target if KO'd and revived while in "Sky" status. The second bug occurs when Cyan is afflicted with the Imp status while in "Sky" status. He counterattacks with a simple physical attack instead of Sky, and as such, "Sky" status never comes off. When combining these bugs, Cyan or Gogo enters an infinite loop of attacking. Because he's an imp, "Sky" status never wears off, and because he was revived after being KO'd, he effectively attacks and counterattacks his own attack with another attack. The loop ends when all enemies are dead.
This bug was "fixed" in Final Fantasy VI Advance, but can still be done in a different way. After dying and being revived, Cyan or Gogo must perform Sky, and if he is an imp he will go "psycho".
There is a bugfix patch that players can use to fix the first bug on the SNES version, which fully corrects the bug unlike in the Advance version. There is also a second bugfix patch that players can use to fix the second bug on the SNES version.