Wiktionary
n. A book publisher that lets the author pay the expenses of publishing up front, leaving the risk of financial failure with the author.
Wikipedia
A vanity press, vanity publisher, or subsidy publisher is a term describing a publishing house in which authors pay to have their books published. Additionally, vanity publishers have no selection criteria as opposed to other "hybrid" publishing models. The term appears in mainstream U.S. publications as early as 1941. In contrast, mainstream publishers, whether major companies or small presses, derive their profit from sales of the book to the general public. Publishers must therefore be cautious and deliberate in choosing to publish works that will sell, particularly as they must recoup their investment in the book (such as an advance payment and royalties to the author, editorial guidance, promotion, marketing, or advertising). In order to sell books, commercial publishers may also be selective in order to cultivate a reputation for high-quality work, or to specialize in a particular genre.
Because vanity presses are not usually selective (at least in the same way a commercial publisher would be) publication by a vanity press is typically not seen as conferring the same recognition or prestige as commercial publication. Vanity presses do offer more independence for the author than does the mainstream publishing industry; however, their fees can be higher than the fees normally charged for similar printing services, and sometimes restrictive contracts are required.
While a commercial publisher's intended market is the general public, a vanity publisher's intended market is the author and a very small number of interested members of the general public. In some cases, authors of a book that is vanity published will buy a substantial number of copies of their book, so that they can give it away as a promotional tool.
Usage examples of "vanity press".
An SFA is a self-financing author, and Manutius is a vanity press.
Like most of the other local guidebooks, it was paper-bound and appeared to have been published by a small vanity press.
I'd suggest that if you're that anxious to get published, you skip agent-hunting or query-letters to publishers and go directly to a vanity press.
If all else failed, I could have Wacky's complete opus printed up and distributed by a vanity press.
I get the impression that this is a self-published affair, or at least coming from a vanity press imprint.