On Sunday, I read two novellas--Miguel de Cervantes's The Dialogue of the Dogs and Marcel Proust's The Lemoine Affair--and although neither is the most cinematic of pieces, the novella seems to offer something that neither the short story nor the novel does.
During the past few years, I've noticed an increase in the volume of novella-length works disguising themselves as novels. Ian McEwan's On Chesil Beach stands as one example, as does any of Philip Roth's most recent novels. Usually, this is a widely-ignored form, since it stands at an awkward middle ground between the short story and the novel. Also, there are production costs involved: It costs a lot less to produce and print a 250-page collection of stories or a 300+ page novel than it does for a single work that runs in the neighborhood of 150 pages or less.
So why should we bother with the novella? I consider pieces that can be read in a single long sitting--think the equivalent of a movie, so between an hour to three hours--to be novellas. At this length, the novella can have the immediacy of a movie while aspiring to the brevity of a short story. And it's likely that the novella is a better fit for readers on the go than the long novel: The physical thing doesn't have the bulk of a novel, and even in an electronic format, it's something that you could finish on a commute or two via public transportation.
Or if you're thinking of before-you-go-to-bed reading, a novella won't leave you at the point where you've been slogging through chapter after chapter for months, only to realize that you no longer recall what happened three hundred pages ago.
On this note, here's the economic argument: A new release DVD, I've noticed, generally costs around $25-30, more for BluRay. The price eventually whittles down to about $10 to $15. Say that's about three hours in length, so you're spending about $8 to $10 per hour of entertainment when it's new, less as it's been out on the market for a while. And the replay value is infinite, or you can take it to a used-movie shop and get store credit or a new movie if you didn't enjoy it. The same thing applies to novellas, and it's the same cost breakdown for the same amount of time (and the trade-in argument here applies to used bookstores!). A novella such as On Chesil Beach by Ian McEwan retailed at around $25 in hardcover, then about $15 in paperback.
Think of the novella as the literary equivalent of the movie. It has to be short and direct, but also expansive. And the form isn't as obscure as we might think. A number of great, classic works--not just Cervantes's Dialogue or Proust's Lemoine Affair--are generally considered novellas: Melville's Bartleby the Scrivener, Doyle's The Hound of the Baskervilles, and Conrad's Heart of Darkness.
As a little (and inexpensive) taste of what novellas have to offer, I suggest you check out two series of books produced by Melville House Publishing: The Contemporary Art of the Novella series and also their series of classic novellas, The Art of the Novella.