First, an allegory is:

...an extended metaphor in which a person...or event stands for itself and for something else...usually [involving] moral or spiritual concepts...

The Middle Ages were a time of great strife in Europe. The most powerful influences were the Roman Catholic Church—wielding enormous power over all of Europe—and the Black Death (the plagues)—that destroyed the very fabric of the culture—regardless of age, gender or social standing.

There was no separation of Church and State. It was the Church that delivered judgment and punishment, settled disputes, etc. However, the Church's primary concern (besides winning believers) was to inform the people of how they should live. The earliest forms of drama, then, were a means for the Church to instruct the people as to how to best conduct themselves. Besides Chaucer's work, there were allegorical plays: morality, miracle and mystery.

The miracle and mystery plays were based on Bible stories and were very simplistic.

Medieval mystery plays focused on the representation of Bible stories in churches...with accompanying...song. 

They began to appear in the 10th Century, eventually leaving the church and moving out into the town square or the market place. Eventually players who were not members of the Church would adapt them. (Ultimately the Pope would prohibit the clergy from taking part in public presentations of these plays, seeing them as more secular in nature.) Their popularity would continue until the 15th Century, when a more modern drama (what we know today) would "take the stage."

Whereas the mystery and miracle plays were forthright; instructionally, they presented evil characters (such as the Devil) as comic figures. However, the morality plays had a much different tone, brought about by the occurrence of several plagues in Europe.

Writers contemporary to the plague referred to the event as the "Great Mortality".

The Church took this opportunity to elucidate the cause of the widespread destruction: man's sinfulness. They also addressed dishonest behavior brought about in the chaos of the plague years.

These plays...

...are a type of allegory in which the protagonist is met by personifications of various moral attributes who try to prompt him to choose a Godly life over one of evil. 

The morality plays emerged from the clergy's attempt to educate the "illerate masses" by adding "acting" to their sermons, whereby the message they were teaching was visually presented as well. Characters were personified and represented the battle between good and evil, choices between good works and sin. They...

...tended to be elaborate...dramatic allegories in which characters representing various virtues and vices confronted one another.

Allegorically, perhaps the most popular of these plays (still presented on stage today) is Everyman. In this play, Death is personified—appearing to every man (and woman) to remind each that death comes to all, and that living a moral life is necessary to be rewarded in heaven—a new idea being considered by society: the concept to prepare for life after death. Morality plays, in general, concentrated on evil. However, Everyman is different in that it focuses more on goodness—made more visible in contrast to the great evil in the world, while promoting the rewards (and hope) of a more moral lifestyle.

Additional Source:

Adventures in English Literature, Harcourt Brace Jovanovich Publishers: Orlando, 1985.