Usually someone might decline a job promotion due to ill health. They had to wait until St. Anselm was sick to get him to agree to be Archbishop of Canterbury; when he was well, he had the strength to resist the offer.
Anselm is indisputably a Big Dog, a Doctor of the Church. Several of the usual elements are found in his story, including the dissolute youth, reluctance to lead, and disagreements with secular authority. I don't mean to imply that the elements are false or exaggerated -- rather, they seem to be helpful in distinguishing a saint from the rest of the pack.
After the Normans conquered Britain (spit!), they put their own clergy into the most profitable spots. When William the Bastard (not my nickname for him -- you can look it up on wikipedia) died, his son William Rufus became king. Little Billy decided that if he didn't appoint a new archbishop of Canterbury, he could keep all its revenue. But when he got sick, he got faith and promised to appoint one upon recovery. Maybe God took the bait -- Billy felt better and Anselm got the nod.
Billy died in 1100 and his little brother Henry Beauclerc became king. Hank wisely invited Anselm to return to his cathedral, but shortly they too were in a quarrel over lay investiture (it's far more lucrative and less lascivious than it sounds). Within a few years, Hank welcomed Anselm back home, ceding to his archbishop the authority to make his own clerical appointments.
As archbishop, Anselm opposed slavery (an unusual position in the twelfth century) and succeeded in getting legislation forbidding the sale of slaves. But his most lasting accomplishments seem to have been his theological and philosophical writings, earning him recognition as the greatest religious mind between St. Augustine and St. Thomas Aquinas.