I should start by saying that vanity publishing isn't all bad. A lot of the fraudsters have been put out of business in recent years. And although a lot remain, there are still some reputable vanity publishers out there.
The trouble, of course, is telling the good from the not-so-good guys. And you're not necessarily going to find that out from their sales pitches.
Word-of-mouth and personal recommendation are probably your best bets. Failing that, go with your "gut-feeling" on whether this company seems reputable or not. If you don't have those things, my advice would be to steer clear.
What is vanity publishing?
When you self publish a novel, you are the publisher (or a company you set up for the purpose is). Yes, you'll have it printed by a printing firm, and you might even employ a distribution firm - but you are the publisher.
Why is that important? Because it means that you own the books you have paid to have printed (which is the way it should be).
If you take the vanity route, you are still the one who pays all the production costs, but the publishers own the books and you just receive a percentage of any copies sold (a higher percentage than you would get from a regular publishing house, admittedly, but nothing like the remuneration you would receive from a genuinely self-published novel).
But wait, it gets worse...
You're probably wondering why anyone hands over good money to the vanity bad boys. The answer, of course, is that they talk a good talk...
The way it works is like this: You read an advert from a vanity publisher in the newspaper or online asking if you have written. (Regular publishers never advertise for submissions.)
You are invited to send them your manuscript and (surprise, surprise) it is accepted with glowing praise. Of course, you will have to pay to have it produced, though the publisher will dress this up by talking about a "partnership" or something similar.
They will basically promise you the earth in terms of anticipated sales, the royalties you can expect to earn, and the like.
But guess what? A bad vanity publisher doesn't make its money from selling your novel. It makes it from the large amount of cash you pay to have small quantities of it cheaply produced. Which means that any marketing effort it makes (if any) will be minimal. Oh, and the bookstores are unlikely to buy a vanity-published title, anyway.
Like I said at the start, there are some reputable vanity publishers out there. It's just tough to know which ones they are without knowing somebody who knows somebody who...(you get the idea).
So if you want my advice, either sell your novel (on your own or via an agent) to a regular publishing house - the kind that never advertises for submissions, the kind that never asks you to pay a penny in costs. Or if you simply want to see your novel in print, take the Self Publishing route.
If you go it alone, never confuse paying a company to print your novel (self-publishing) with paying one to publish it (vanity).
Don't say you haven't been warned!