I talked a while back about running martingales. An Irish martingale is...literally just a strap with two rings on it that connects the two reins.
The Irish martingale is also sometimes called the semi-martingale. It is most commonly seen on racehorses and its primary purpose is to prevent the reins from going over the horse's head (which can be dangerous) in the event of a fall. Unlike the running martingale, it does not affect the horse's head movement. Thus, it is generally used on horses that won't tolerate the action of the running martingale and, sometimes, by riders that feel martingales interfere with the horse too much.
Irish martingales are also considered a bad idea for dressage as they hold the reins together and prevent some aids from being used.