The late Roman philosophical text The Consolation of Philosophy, by Ancius Manlius Severinus Boethius, was an extremely well-known and highly respected book in Chaucer's time. It was considered a must for most schools, and there were very few learned people who had not read Boethius's work and the ample medieval commentary available on the book and its subject.
The work shows, in erudite and polished Late Latin, a philosophy of inner fortitude that would enable the practitioner to suffer any indignities of Fortune without regret. It is prison literature, written while Boethius was imprisoned for treason. The work is meant to show the soul the way to true knowledge and wisdom, exhorting the reader to shuffle off the cares of this world and perceive only the true and lasting things of Heaven. The crux of the argument is the discernment between partial, contingent, and apparent "goods" (that is, good things), and the one, true good which is God. It has a powerful internal logic, and it still has a great deal of influence as a work of philosophy today.
Chaucer uses Boethius's image of Fortune and her wheel in The Book of the Duchess. This was a well-known image in his time, and it would have been nearly a requirement in an elegy like this poem, for it would demonstrate that, while the loss of Lady White (or, Blanche of Lancaster) was indeed tragic, the turn of Fortune's wheel happens to all people, and it must be borne and understood within the context of the one, true good. Boethius asserted that when human beings put too much faith or love into the contingent, partial, or apparent goods (which includes essentially anything that is material or of the earth, including intangibles like love of family or one's health), then sorrow will always be the ultimate result. But the wise person who puts all of his or her faith and love in God and Heaven, the essential and permanent things, is never saddened, for the good of God is never apparent, partial, or contingent upon anything, and it cannot be taken away by Fortune.
During a time when most people had considerably less control over their lives than we do today, this philosophical idea was no doubt a "consolation." Today, people still turn to religion and philosophy to find something lasting and permanent in a fleeting world. Thus, the value of poetry itself has been treated with skepticism by some philosophers and Christians. The key consolation, at least, is to know the difference between the fleeting and the permanent, even if one does not possess the permanent things. This principle at least helps people judge their own situation and put it in perspective.
The work of Boethius was highly regarded, but it was becoming apparent that during Chaucer's time fewer people were reading it in Latin. There was a general call for an English translation, and Chaucer provided one (also, partially, using the French tranlation of Jean de Meun). Chaucer's translation shows signs of the immense care that he took to strictly adhere to the original, and, though some of Boethius's poetic passages were rendered into prose, Chaucer did so in order to clarify the sense in English in the most direct way. Chaucer's version was used by his contemporaries, and at least some copies made it into medieval schoolrooms.
