Simply put, the fastest way to mail something within the
United States. If it needs to get there faster...well, that's what
the internet is for, isn't it?
This is a service provided by the United States Postal Service for extremely fast delivery within one day, or two if it's a particularly remote location you're sending to. Basically, if first class mail just isn't fast enough, you send it express mail. Comes complete with $100 of insurance, en route tracking, all the mailing materials you'll need at no extra charge, and a money back guarantee if it doesn't get there by the guaranteed time. Optional services include return receipt, more insurance for an additional fee, and C.O.D..
The snag is simple - you take your express mail article to the post office by a given time, and then and ONLY then will they guarantee the delivery in the given time. You can find out what that is by calling said post office - it's usually 15:00-16:00, depending on how remote you are.
There are simple reasons for this guarantee thing. Your courier's work hours are from early AM till whenever they finish the route, and that could be after the cutoff time. Also, your curbside drop boxes are typically collected from no more than once per day, and in many cases this is late afternoon. By the time they get to the office that processes them, hey, guess what, you missed your flight. So the only way to really guarantee this and hope you can get that refund is by going to the post office with your article.
Base/Flat rate for express mail is $13.65 (Flat rate is assuming you use their flat rate envelope, a pressboard envelope with "Express Mail" artwork emblazoned upon it that will generally hold no more than 200 pieces of 20# paper), and it goes up from there depending on how much it weighs or how much you need it to be worth in case of lossage.
EDIT, 14Oct2005 - Sunday/Holiday service is no longer offered, and apparently hasn't been offered since 9/11 due to security and economic concerns. FedEx, at this time, is the primary air courier for the mail, and owing to the fact that FedEx doesn't operate on Sundays and Holidays (flight schedules aside), unfortunately, neither can Express Mail.