The late medieval morality play Everyman is a typical work of the middle ages for a number of reasons.
In the first place, the play is explicitly Christian in its meanings and purposes. Since the middle ages were an era in which Christianity was the dominant (indeed, almost the exclusive) force in western European religious thought, it is not surprising that this play quite openly addresses Christian themes and conveys a Christian message. Most plays written during this time were written to teach Christian history (as in dramatized stories of the Bible) and Christian morality. For these reasons, Everyman is an utterly typical play of its period.
However, it is worth stressing that the kind of Christianity emphasized in Everyman is Roman Catholicism, which was the specific dominant brand of Christianity in western Europe at this time. The Protestant "Reformation" had not yet occurred, and Protestants would have been bothered by this play's emphasis on good works, the power of the priesthood, and the need to confess one's sins to a priest.
At the same time, Everyman, like many other works of medieval literature, shows a genuine awareness of the various failings and partial corruption of the Catholic church during this period. One of the most interesting episodes in the play is the passage in which the character Five-Wits extols the power of priests and the priesthood, only to be followed immediately by Knowledge, who explains that many contemporary priests are hypocrites and sinners (729-69).
In addition, Everyman is also typical of medieval literatture because it announces quite openly, in its very first lines, that it will be a didactic work -- that is, a work intended to teach. Much medieval literature is similar in being very explicit in its intent to impart moral lessons.
Furthermore, Everyman deals with one of the fundamental themes of medieval literature -- the theme of mutability, or the idea that all things on earth, including humans, are subject to change and decay. Only God and heaven could provide a source of eternal escape from such pervasive, usually negative change. Everyman teaches this lesson quite explicitly.
Moreover, Everyman is also a typical work of medieval literature because of its heavy emphasis on the inevitability of death (the most important kind of earthly mutability). A character named Death actually appears in the play, and death is a major theme of the work. The power of death is a very common focus of texts of the middle ages, and if is definitely a major focus of Everyman.
Everyman also resembles some of the other great works of the middle ages (especially The Canterbury Tales, by Geoffrey Chaucer) in combining humor with a serious moral message. This tendency is typical of medieval thought, which often saw human life as ridiculous and laughable when viewed from a cosmic Christian perspective.
Therefore, in all these ways and many others, Everyman is a highly characteristic work of its era.