The paralysis trap tile will be linked to several nearby gas vents hidden in the floor. When the trigger is stepped on (or an item is thrown onto it) each vent will release a quantity of paralysis gas. The gas will appear only on the vent tiles, but expands quickly in the first few turns after the trap is triggered. In order to avoid the gas, you can either try to escape from it (a Scroll of Teleportation or Staff of Blinking will probably be required in order to get away fast enough), or set the gas on fire.
For players with armors possessing the Respiration intrinsic, intentionally activating paralysis traps provide an easy way to immobilize strong enemies for easy kills, without risking death for the player.