1. Allusion
Literary Device

2. From WikiAnswers http://wiki.answers.com
An allusion is:
A reference to an historical or literary figure or event. Example: I am no Prince Hamlet.
Answer
Often confused with illusion, an allusion is a literary term that refers to a reference in one literary work to another literary work.
E.g. The Simpsons television show constantly refers to (some may say, steals from) movies, music, literature etc. In a scene where Principal Skinner is in his office, he suddenly turns to his window and looks out at an old, spooky house while he talks about a tormented relationship with his mother.
This is an allusion to the Norman Bates character in the movie Psycho.

3. More from WikiAnswers
Another example of an allusion would be "The girl's love of sweets was her Achilles heel," referencing the warrior in Greek mythology, Achilles, who could only be harmed if something hit his heel because he was dipped in magic water as baby when his mother held him by a heel. Achilles' only weakness is his heel, so an Achilles heel reference means a downfall or weakness, in this example a weakness for sweets.

4. Another more academic definition http://www. spiritus-temporis
In rhetoric, an allusion is a stylistic device in which one implicitly references a related object or circumstance that has occurred or existed in an external context. An allusion is understandable only to those with prior knowledge of the reference in question (as the writer assumes the reader has). An "allusion" is not the same as an "illusion".

5. Another Example
An even more recent example in popular culture was cited recently in The Matrix Reloaded, wherein Morpheus states, "I have dreamed a dream, but now that dream is gone from me (sic)", which alludes to a quote by King Nebuchadnezzar from Daniel 2:3 of the Old Testament. This is known as a religious allusion.

6. More Understanding
An allusion is an indirect reference to a person, event or piece of literature
Allusion is used to explain or clarify a complex problem. Note that allusion works best if you keep it short and refer to something the reader / audience is familiar with, e.g.:
famous people
history
(Greek) mythology
literature
the bible

7. Good Reasons for Allusions
If the audience is familiar with the event or person, they will also know background and context. Thus, just a few words are enough to create a certain picture (or scene) in the readers minds. The advantages are as follows:
We don’t need lengthy explanations to clarify the problem.
The reader becomes active by reflecting on the analogy.
The message will stick in the reader's mind.
Examples:
Don’t be a Scrooge (allusion on the rich and mean Ebeneezer Scrooge from Charles Dickens Christmas Carol)
The software included a Trojan horse . (allusion on the Trojan horse from Greek mythology)
Plan ahead. It was not raining when Noah built the Ark . (Richard Cushing) (allusion on the biblical Ark of Noah)

8. Examples you may know
Many allusions on historic events, mythology or the bible have become famous idioms.
Examples:
to meet one’s Waterloo (allusion on Napoleons defeat in the Battle of Waterloo)
to wash one’s hands of it. (allusion on Pontius Pilatus, who sentenced Jesus to death, but washed his hands afterwards to demonstrate that he was not to blame for it.)
to be as old as Methusalem (allusion on Josephs grandfather, who was 969 years old according to the Old Testament)

9. We Didn’t Start the Fire
Billy Joel’s song is full of allusions.
Listen and follow the words
Use the activity in SpringBoard to study the song’s allusions and learn for yourself.
The Poison Wood Bible holds many allusions we will discover together.

10. We Didn't Start the Fire

11. Background
Joel explained that he wrote this song due to his interest in history. He commented that he would have wanted to be a history teacher if he had not become a musician. Unlike most of Joel's songs, the lyrics were written before the melody, owing to the somewhat unusual style of the song. Nevertheless, the song was a huge commercial success and provided Billy Joel with his third Billboard #1 hit.
"We Didn't Start the Fire" was written by Joel after a conversation with John Lennon's son Sean. Sean was complaining that he was growing up in troubled times.