As a conceit can be defined as an elaborate metaphor, and Spenser claimed "dark conceit" to be a synonym of "continued allegory," he uses the term to define the nature of his book as an allegory.
An allegory uses characters as symbols, often to express a moral or political truth. In his case, Spenser uses the story to express ideas about Elizabethan politics, while certain characters represent different religious virtues.
In his introduction, written as a letter to Sir Walter Raleigh, he says:
Sir, knowing how doubtfully all allegories may be construed, and this book of mine, which I have entitled The Fairy Queen, being a continued allegory, or dark conceit, I have thought good, as well for avoiding of jealous opinions and misconstructions, as also for your better light in reading thereof, (being so by you commanded,) to discover unto you the general intention and meaning, which in the whole course thereof I have fashioned, without expressing of any particular purposes or by-accidents therein occasioned.
He uses the term to aid his readers in understanding the meaning behind the story; thus the poem does not mean explicitly what it says, but rather requires interpretation, which also leaves open the possibility for misunderstanding.
This blog post does a good job to explicate the individual allegorical characters' meanings: