What have the Irish ever done for us? (Quite a lot, actually)

The Roman Empire never reached Ireland. Partly for that reason, neither did the Christian gospel, until the 5th century when first Palladius, and later Patrick were sent as missionaries to the people of Ireland, known as Gaels or Scoti. 

I have told the story of Patrick elsewhere, but suffice it to say that, born in a Christian family in Britain (his father was a deacon), Patrick was taken captive by Irish pirates and spent many years held against his will before escaping and eventually ending up in what is now France, studying at Auxerre. Patrick was called by God to bring the gospel to his former captors, and the conversion of Ireland to Christianity is associated with him. 

At that time, Ireland had few if any cities, and the backbone of the Irish church was the monastic movement with a network of monasteries in places such as Foyle (near Derry/Londonderry) and Bangor. In the year 563 a young monk called Columba (Colum Cille), left the monastery at Foyle (near Derry) and sailed, along with 12 companions, across the Irish sea to Iona, which at the time was part of the same kingdom of Dál Riata. Exile from one's homeland was considered both an act of penitence and also an opportunity for Christian service: they were "exiles for Christ's sake" (pelegrini pro Christo). On Iona, Columba founded an abbey which became a base for evangelising the Picts who inhabited what is now northern Scotland (see painting right). Later, the monks founded another major monastery at Lindisfarne, off the eastern coast of what is now Scotland. This became a base for evangelising the kingdom of Northumbria, where the inhabitants were ethnically Angles (of Germanic extraction) and pagan in belief. One of the most famous missionaries was Aidan, who was able to communicate the gospel simply and gently to his pagan hearers. English was not Aidan's native language and, initially, the Northumbrian king interpreted for him.  

Later, in 590, another Irish monk called Columbanus set sail from Bangor, likewise with 12 companions, arriving in what is now France where he and his companions set up monasteries, such as the one at Bobbio, and reached out to the nominally Christian or pagan inhabitants of Europe. Gall (d.645), for example, worked in what is now Switzerland. Killian is known at the Apostle of Thuringia and Franconia.  

This intense period of Irish missionary work lasted until the death of Virgil in 784. In a later phase, there was further Irish influence in the later medieval period. Throughout Central Europe there are many Schottenkloster (Scottish, i.e. Irish, cloisters), which date from this time. From the 690s, the recently converted Anglo-Saxons had a similar period of mission, lasting until the late 700s.