Traditional allegorists, such as Origen, Clement, and Philo, did believe in the historical events of the Scripture they allegorized. This makes them quite different from more recent allegories such as John Bunyan's Pilgrim's Progress, C.S. Lewis' Pilgrim's Regress, or Spencer's The Faerie Queen. Note that none of these authors are allegorizing Scripture, they are writing allegories based on their journeys or to teach one how to live a virtuous life.
An allegory is a metaphor extended into a story (Kaiser and Silva, An Introduction to Biblical Hermeneutics, pg. 94). In an allegory, items and characters in the story are used to convey truth about a person's spiritual journey. The elements of the story will take on characteristics which are quite different from their literal meanings. In Scripture, Proverbs 5:15-23 is a good example of allegory.
Drink water from your own cistern and running water from your own well...
(Unless otherwise stated, all quotations are from the NET Bible.)
Here, the allegory teaches marital fidelity through the example of drinking from your own well. Whether or not parables are allegory is debated. Admitting that allegory exists in Scripture is quite different from allegorizing Scripture. Allegorists often speak of eliciting the deeper, spiritual meaning of Scripture.
One must be careful to distinguish between allegory and typology. Typology is also comparative ("this" represents "that") but the comparisons are less stretched and more rooted in the historical event. For example, John 3:14f uses typology . . .
3:14 "...Just as Moses lifted up the serpent in the wilderness, so must the Son of Man be lifted up,
3:15 so that everyone who believes in him may have eternal life."
. . . to compare the crucifixion of Jesus to Moses lifting up the serpent in Numbers 21:4-9. However, allegorical connections are often strange. Philo of Alexandria, a Jewish historian/philosopher/theologian would see a discourse on the four virtues from the four rivers in Eden. Similarly, Clement of Alexandria saw a warning to shun various vices from Moses' prohibition against eating unclean animals. Typology requires that the event happened in history and points to something else.
Typologists do not believe it is the only true exegesis (merely one for application and use) and is not the only way to arrive at the spiritual truths of Scripture. Allegory does not care whether it happened or not. In that sense, Origen at times is more of a typologist.
Contrary to Clement, Origen (185-254) (also a member of the Alexandrian school of interpretation), saw three levels in Scripture. He assigned them body (literal), soul (moral), and spirit (doctrinal). Clement had seen only two, body (historical) and soul (spiritual). Origen considered the body/historical meaning inferior to the other two, which are accessible only through allegorizing. Most likely, Origen would have called his method spiritualizing. At times, his exegesis is a mixture of allegory and typology. Nevertheless, there is no doubt that Origen saw allegory as the true exegesis and the only way to uncover the deeper spiritual truths of Scripture (Mickelson, A. Berkely. Interpreting the Bible, 32; Ramm, Bernard. Protestant Biblical Interpretation. 33; Grant, Robert M., and David Tracy. A Short History of the Interpretation of the Bible. 55-56).