One advantage to using D&D is that the "story" of D&D is well known. D&D is fundamentally a game about going into a hole in the ground, facing monsters, killing them, and taking their stuff. That's not to say that all D&D campaigns resemble that--but let's face it; most do. And to the extent that they don't, they need explaining away from those expectations in order for them to work. I would say that this is one of the main reasons why D&D is so easy for people to run--what the game is about, what the PCs are going to likely be doing, and what the implied setting is like--all of that is well-known without you having to say anything.
So, if you're going to run a fantasy game other than D&D, unless it's in a setting that's well known from some other medium, you'll have to communicate that clearly and concisely to your potential players. Which also means that you'll have to make sure that you have a solid handle on what your game is going to be about. What's the "story" of your game? By that, I don't mean that you already know what's going to happen throughout the campaign, of course. I mean, what is the game about, who are the PCs likely to be, and what are they likely to be doing, in broad terms.
This is especially important in games or settings that are likely to be unfamiliar to your players, since otherwise they won't have any clue as to what kind of characters to envision or what the game is likely to entail.
In one of my campaign briefs for the two potential DARK•HERITAGE games that I wrote up, I wrote that the theme of my game was: "The Black Company and The Godfather meets Sergio Leone and Pirates of the Caribbean. Swashbuckling fantasy action meets investigation and horror. Sword & sorcery on the surface, but just below that, this is Call of Cthulhu. Intrigue and investigation are more important than High Fantasy conventions. This is sword & sorcery noir, with a strong dose of horror and the occult. This particular campaign takes place in the northern area of the setting, which is more like the American Old West would have been if sabertooths and mammoths and all that jazz hadn't gone extinct. Flintlock guns, prides of hungry dire wolves, nihilistic, hidden cults, savage tribesmen amid islands of civilization--the leftovers from a crumbled daemon-touched empire of the past--that's the setting in a nutshell."
Here's another example from some of the preview material Wizards of the Coast gave us for Eberron after it had been selected in the Great Setting Search and before it had been officially released: "The setting offers a traditional fantasy world filled with pulp noir-style action and adventure delivered with cinematic flair. Keith (Baker) described it in his original one-page propasal as being like "Lord of the Rings meets Raiders of the Lost Ark and Maltese Falcon." If you can imagine what your favorite Dungeons & Dragons adventure would be like if it were turned into a hollywood action-adventure block-buster, you've got an idea of the kind of experience your characters will have in Eberron."
That's a great start. It covers much of what I want to communicate. In fact, the Eberron one makes mine look a little wordy and repetitive. But how do you come up with a campaign theme that's strong enough to suggest adventure of the kind you hope to run, as well as communicate to the players what kinds of PCs they should make? What kind of elements to a good campaign theme should you include? What needs to be communicated, and what needs to be "held back?"
First off, I think a good campaign theme could and should include the following elements:
1) You should be able to sum it up in just a few sentences. If it's too complex to fit into a simple paragraph about the length of one of the two samples above, it's too complex period, and needs to be further distilled. Note, of course, that that doesn't mean that your setting can't be complex. Just that you need to be able to describe the theme of it fairly quickly. In fact, not only should you be able to sum it up in a paragraph, but you should be able to sum it up in the opening sentence or two of your paragraph, with the rest just adding a bit more color and detail. For DARK•HERITAGE, for example, the sentence, "Swashbuckling fantasy action meets investigation and horror," sums it up in a single sentence. For Eberron, "The setting offers a traditional fantasy world filled with pulp noir-style action and adventure delivered with cinematic flair." does much the same thing. Curiously (or not) you'll notice some similarities in gross thematic description between my setting and Mr. Baker's. That's not entirely coincidental--my feeling that Eberron was a great idea that was partly hampered by being too closely tied to D&Diana was one of a couple key inspirational realizations that had me striking out on my own in this direction. But that's neither here nor there.
Both of those summaries convey to the players what kinds of activities the campaign expects to cover, what kinds of characters it expects to entertain, and it does so in a single sentence.
2) A good way to convey this in another way that will also reach your intended audience is the "Hollywood pitch" idea, which I've talked about before. Compare your campaign to some properties or concepts or ideas that the players should already be familiar with. For example, "The Black Company and The Godfather meets Sergio Leone and Pirates of the Caribbean." or Eberron's "Lord of the Rings meets Raiders of the Lost Ark and Maltese Falcon." Be careful not to compare too many disparate elements, or elements that are not as likely to be as familiar to the players. Unless your group is made up of a really esoteric and eclectic crowd, for example, "Dostoevsky's Crime and Punishment meets James Joyce's Ulysses and ancient Tuareg mythology" isn't likely to be very helpful (nor is that game likely to appeal to many players, but that's neither here nor there.) Again; the point of this is to convey in simple shorthand what the PCs are likely to be like, what kinds of things they are likely to be doing, and what what kind of tone and feel the game will have. It's important that any "Hollywood pitch" type comparisons utilize ideas or properties or titles or franchises that have a strong feel of their own. The Maltese Falcon or The Black Company or Raiders of the Lost Ark or Sergio Leone are famous for their tone and feel, for example, making them better examples than more "wishy-washy" concepts.
This is also your chance to "sell" the game a bit. Try and get your players excited to be playing it. It doesn't just have to be dry and descriptive; in fact, it shouldn't be. This is a great example to point out where you think the game will be similar to things that your players (hopefully) already love.
3) Any other ideas that are helpful without being overly wordy and detailed. I included a bit about sabertooths and mammoths, for example, just because it was easy to say and conveyed a great deal of information--exotic and dangerous animal life and wilderness exploration is an important part of the game; it's not just urban intrigue or whatever.