Dante's Divine Comedy enjoyed enormous success. However, it should be noted that it was not translated into other languages until much later. Thus, strictly speaking, its 14th century readers were Italians, and a small minority of foreigners that understood Italian.
One reason for the poem's popularity lies in the fact that it was written in "vulgar" Italian, which made it accessible to any literate person. By contrast, authors of major works of the times thought that they would lose quality unless they wrote in Latin.
Moreover, the Church was undergoing a major crisis, marked by corruption and political strife. Dante's depiction of unpopular or much hated characters suffering the tortures of Hell vicariously avenged the wrongdoings suffered by the population.
Although The Divine Comedy is ultimately a very complex allegory not easily grasped, comprehension of its most obvious themes sufficed to turn it into a favorite with his contemporaries.