I've read this book and frankly I'm not too impressed with it. It's 213 pages, out of which maybe 40 are actually relevant to this question. The author rambles on about Ausonius and St.Augustine for 50 pages, about the ancient Irish for 50 (specifically the Tain-an Irish epic), St.Patrick for another 50. He finally answers the question in the title of the book by page 180. It's easy to read, but it's also extremely Eurocentric, and manages to insult the Germans, the Mexicans and the intelligence of the reader (by assuming that the reader would not be able to read Plato). It is also rather disorganized. If a university student would present this book as a scholastic essay, he/she would get a pretty poor mark.
Anyway, the gist of it is that the christianized Irish sent out missionaries in the 6th to the early 9th centuries, which founded monasteries in the rest of Europe, mostly in Britain, France and Germany, which eventually became centers of knowledge.
It does have some good information though. The Irish monasteries were the centers of culture and learning; much Latin literature was saved by being copied there. The Irish had a culture which was much more liberal than the rest of Christian Europe, expecially the status of women. One of their major contributions to the Catholic church is the private confession. The political structure was a sort of confederacy, where hundreds of petty chieftains (called "Kings"), elected one of their own for a year to be the High King of Tara: more of a symbolic figure than anything else. Lacking in urban centers, with the arrival of christianity, the true center of power in the land passed on to the abbots.The end of this golden age of learning in monasteries and sending out missionaries came at the beginning of the 9th century, with the Viking attacks.