How can I break up a lengthy explanation?

Phil Farrand of The Nitpicker's Guide to Star Trek called this "being the cabbagehead." Certain information had to be revealed to the audience, but it was information which the characters would reasonably already know.

So the writers picked someone in the room to be the "cabbagehead," meaning someone developed the I.Q. of a cabbage and everything had to be explained to him or her as though s/he had never gone through Starfleet training and years of spaceflight experience. (Counselor Troi got this role a lot on TNG.)

Practically speaking, you set things up so one or more of your characters is woefully uninformed about whatever it is, and the more informed character(s) have to enlighten the cabbageheads. As far as technique, Kate and iajrz both have excellent suggestions.

If the explanation is interesting, the reader will not notice that is is long. If it is not interesting, breaking it up will not make it interesting.

So forget about whether it is too long and focus on whether or not it is interesting. The reader may be interested in explanation for one of three reasons:

1. They are interested in the thing being explained. When you explain weapons in a thriller or forensic procedure in a mystery, many readers will be interested in these things independent of their role in the story.

2. They are interested because the explanation is so gripping that it creates interest simply because it is so good.

3. They are interested because the explanation makes the story make sense.

It is important to get the order of things right with these. You may want to give an explanation up front in order to make the story make sense when the reader gets to it. This is not a case of number 3. For number 3 to apply, the reader has to already be in the story and sufficiently committed to it that they are hungry for the explanation so that they can go on with the story. If you want the explanation to come before the story, then you have to make it either number 1 or number 2.

Number 1 requires knowing your audience and knowing your stuff.

Number 2 requires being a genius.

It sounds like you're describing an infodump (warning: TV Tropes), and that's a phenomenon best avoided.

The issue is this: by your own description, the explanation is not interesting enough to hold the reader's attention at length; its purpose and significance will only be clear to the reader later in the story; and in this particular instance, it's also long. You can see why this doesn't make for a great reader experience. It's as though you've got a brilliant, hilarious joke, that only makes sense if you read the first 3 pages of the phone book - and you can't tell your friends why they need to read the pages until they're already through them.

Here's the key: Avoid writing scenes which the reader has no immediate, compelling reason to want to read. So if you're determined to write up a history lesson, you'd damn well better make sure that, at that point, the reader is dying to hear that lecture. Your other main option is to avoid the lecture entirely by conveying the backstory in other, more compelling ways, usually intertwined with the story and the action. I'll touch on both these options.

Prepping the reader for exposition

The idea here is to give the reader a strong interest in the details you want to expose. Then they're perfectly happy to listen attentively - they know exactly why they should be interested.

• Mysteries of all stripes are based heavily on this approach - solving the case provides a tremendous incentive for the reader to sit through any length of otherwise-dull exposition.
• Sometimes you can make the lecturing character play hard-to-get - basically setting up his information as being hugely important, refusing to reveal it, etc. If you manage this effectively, such a ploy can convince the reader of the exposition's importance.
• The interest doesn't necessarily have to be plot-related or functional - if the details are charming, lyrical, amusing, controversial, etc., that's often enough to maintain the reader's interest and give him a justification for the piece.

In The Matrix, Morpheus explains to Neo what the Matrix is. This is straight-out exposition and backstory, but it's one of the coolest, most memorable scenes in the movie. Observe how well the movie establishes that this infodump will solve a question we want answered ("What is the Matrix?"), and that this question is crucially important and monumental (observe all the effort and intrigue and escapades that all sides expended to get Neo this information or to keep it from him). The scene itself is also beautifully presented - Morpheus doesn't just explain; he demonstrates, he brings in cool, colorful stuff, he makes the explanation fast-paced and action-like even when there's nothing actually going on.

One proviso is this: differentiate between the reader's interest in the exposition, and a character's interest. For example, you might have a pupil-mentor dynamic between two characters, with the pupil desperately eager to win the mentor's respect by learning well. The reader will be invested in the pupil's goal - but that goal is pleasing the mentor, not learning the material. That's the means; the details themselves don't interest the reader. If you want the reader invested in the details, then you've got to give him a reason to care about them.

Weaving exposition into plot

The Turkey City Lexicon refers to this as "Heinleining." The idea is that you avoid the need for a long lecture, by having the details you want to expose show up as significant details in the plot without ever stopping the action. How do you do this? Well, if the details are really that significant, unique, and world-changing, then they probably affect the world in more ways than one. If the Goddess Fifthemia is locked in eternal conflict with the Thermal Demigod Extrynius, then that might well have resulted in the Mythaline Cult creating the Gem of Hypothermia, which is the focus of your story - but probably some other people have noticed and been affected by the issue too, hmmm? So you could portray Fifthemites being bigoted against Extryites, or one of the characters could be an atheist whose farm is declared as holy ground by both gods, and he needs to decide which priest to sell it to. And those are scenes which justify exposition immediately, as you go along - often, trickled in bit by bit, so the reader doesn't even notice he's being exposed to.

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Whichever option you choose, I think you'll have found the answer to your question, because the explanation will no longer be a monologue that needs to be broken up into pieces. It will be a scene, with conflict and emotion and goals and reaction; those are constantly present and keep the explanation from turning into a lecture. As a scene, intertwined into the larger story, it might also be taking place in the middle of some larger event - in the middle of a battlefield or a football game or a demonic convent or a snowy hidey-hole in which the characters are waiting for Santa Claus, and all those also serve to keep the explanation from becoming monotonous.

Bottom line: the best way to avoid boring the reader is to write scenes, not explanations. The good part of this is that, with a bit of planning and creativity, explanations can be made part of scenes - and twisted into something much more interesting and compelling than they could ever be on their own.