A while back I was watching someone play through Devil May Cry 4, and there was an interesting bit of dialog that ocurred after a battle between the half-demon Dante and a mad scientist villain who'd come up with a way to attain massive amounts of power by turning yourself into a demon. I'm paraphrasing, but basically the lines went something like this:
Glasses McStuttery: Impossible! How can there still be such a gap between your abilities and mine?
Dante: You sacrificed your humanity. It's that simple.
Now, the scene goes on to basically imply that "humanity"=having a heart, caring about people, fighting for Twoo Wuv, etc. and that it'll always win out in the end. But Dante's blunt reprimand had already sent me off on my own mental tangent. See, it's always bugged me that the soul had so little meaning in Dungeons and Dragons- it could be a huge part of the fluff, but crunch-wise it's no more than an explanation for things like Level Drain. The only time it really comes up is when you're trying to rule about whether someone can be raised and so on. And it's not just D&D- selling your soul is a classic concept at the core of western supernatural fiction. So why is it always left so vague? Here's how I would approach it. . .
In this. . ."cosmology" seems the best word. In this cosmology your soul is the source of your humanity and mortality- when you grow as a person, develop in a way that goes beyond memorizing trivia or lifting weights to bulk up, your soul is the key. Your experiences are the paint, your soul is an infinite canvas and you are the picture.
The forces of heaven and hell, demons and angels- these beings are not created with souls. They are immortal, and many attain incredible power, but most do not "train" or "learn" even though they are completely sentient. The only way for such a being to develop on their own is to get their hands on a mortal soul, and that is something one can only relinquish willingly. This is why the forces of hell are so willing to bestow untold pleasures upon someone who would sell their soul, particularly a heroic character who has proved their soul's strength- to them the forces of hell will gladly give power. Think of it from a player-character's perspective; snap your fingers and bam, you've got the half fiend template, no further obligations or mandatory alignment change. The forces of hell will give you even more power- more ability score increases and supernatural abilities- as payment for additional services, but that's only if you're interested. Tempting, no?
To speak plainly: Without a soul, you stop gaining experience points. Simple as that. You usually don't feel any different at first- you're just as strong and smart as you would be otherwise. But your skills, personality, maturity, alignment- those things will now remain unchanging, like a blooming flower that you pluck and press. You no longer age, though you can still be killed or die of disease- and that's the end of the story. There is no "what happens after you die", because in every sense that matters there is no "you"- just a brain and a body, going through the motions.
And of course, the forces of evil aren't the only ones who can use souls. An angel can make the exact same bargain. In several good-aligned religions this is seen as an ultimate act of devotion; not something that all should aspire too, but rather an act that goes even further (Some would say too far). Several times, different factions and good-aligned deities have clashed over when (if ever) it is right to accept such a gift and whether they have the right to ask it of their mortal devotees.
So a demon or celestial who gets a soul can now gain class levels. Just another sort of power to give their side an edge in the eternal war, right? Most outsiders think so- now they can acquire new skills mortals can- but its not quite so simple. See, as soon as they acquire a soul, their fundamental nature is no longer static. The "Always" preceding their alignment disappears, and they even begin to age (albeit slowly). Fallen angels and redeemed devils- normally such a deed is done artificially, by warping their nature with magic. Such methods won't work on an outsider with a soul, which quickly reverts to its true nature; but these outsiders are now fully capable of 'deserting' on their own. A soul is a dangerous thing; a wise outsider never takes such things lightly.