It's a short letter written to an agent or publisher/acquisitions editor to highlight and sell your book.
Writers can query both written and unwritten material; it can be used to sell an idea for a book that an author will write if contracted by the publisher, but most commonly is used to sell a finished written manuscript.
It's the first impression someone who may buy your work gets of your MS, and it's critical. You don't get to query again with that person or company if they reject (although there are extenuating circumstances). It may also lead to an agent or publisher requesting to see your actual MS, or a partial example of it like the first three chapters or so. That's why this is such a big deal...if you screw it up, you won't make a sale.
Even though they're not long, query letters can be hard to write, and have to be done right. So, I have this little book to help me. I also have a good support network of writers to ask to critique my query, because there's no better way to get good advice than from people who have done it before.
Most querying is done online via email these days. That's probably better; the response time can be quicker, and there's less of the dreaded waiting game. It's also more environmentally friendly...if they request a partial or full MS copy, it's just a click away instead of an hour at the photocopier and post office.
There's no way around querying...you just can't avoid it. So you just do the best you can, and hope you market your book in the best way possible.
Have you queried?