Good points by the previous posters. This is a classic American story, covering the stages of life from birth to death and everything in between. It's allegoricalin this sense: while this is set in a rural town in the early 1900s, it is everyone's story. Who hasn't had the classic friend misunderstanding, or the acquaintancewho died too young, or the fellow church member who has "issues," or cried at a wedding, or lost a loved one. And who isn't moved by the idea that we live too quickly, without really looking at one another, as Emily says to her mother. It's everyone's story, and that's what makes it an allegory.
I agree with everything in the first answer but I'd like to add that an allegory also has some kind of moral message. In this case the message is to appreciate life while we have it, for life can be brief. The three acts of the play represent three stages of life---youth, adulthood and death. However, death is never really mentioned until Act III and Emily never seems to appreciate life until she goes back to try to relive it. That's why Emily asks the anguished question, "Do any human beings ever realize life while they live it?" The stage manager is quick to answer, "No. He pauses and says, "The saints and poets, maybe-- they do some. In other words, everyone takes life for granted at some point. When the stage manager says this, the audience realizes the symbolism for the rest of the characters and the reason for the unusual way the play is staged. The bare stage reminds us of the lack of importance of material things and the importance of relationships---something very common in other allegorical works.