Of the eight Irish breeds, four are terriers, which suggests that either Ireland is overrun with vermin, or that the Irish are obsessed with ridding their country of small four-legged critters and repopulating it with small four-legged critters that bark.
The Glen of Imall Terrier originated in the Glen of Imaal in County Wicklow. This may be why it's called the Glen of Imaal Terrier, but this hasn't been verified. In addition to the terrier's traditional vermin quarry, this breed also hunted foxes and badgers. A description at glens.org states:
The European badger weighs in at 40 lbs and the Glen was tough and strong enough to go to ground and dispatch the vermin soundlessly.
The article doesn't indicate if this was done with knife or garrote.
The Glen was also used as a Turnspit Dog. That is, it would walk on a wheel that would turn a rotisserie on which dinner was cooking. This is why the overwhelming majority of Glen of Imaal Terriers today are employed as barbecue chefs.