I'm glad you followed this link, but I'll be surprised if you read the whole thing! I've spent a good chunk of the last 12 years of my career using, testing, and contributing to the developement & promotion of these things, and am often asked what they are.
A lot of times on TV, you'll see musicians who look like they're wearing hearing aids. Well, those are In-Ear Monitors (IEM's). IEM's are headphones which fit into your ears. They use tiny drivers (speakers) encased in an enclosure which is custom-molded to fit your ear canal. I know that might sound a little creepy, or even unsafe, but it's neither.

IMPRESSIONS
In order to ensure a proper fit, you go to a registered audiologist who is familiar with IEM technology, like my friend Rhonda Martin, Executive Director of the Toronto Musician's Clinic. IEM's are custom-molded to go "just past the second bend of the ear canal", and the audiologist does "impressions" of your ear canal to that point. That's precisely the best point of delivery for IEM's. The audiologist then sends the impressions to the IEM manufacturer of your choice.

MANUFACTURE
This is done by a number of companies which specialize in the design & manufacture of IEM's. They make models with one driver for each ear (stereo), and models with two drivers for each ear (high frequency & low frequency, stereo). It's amazing that they can put two drivers in each ear, but for the real high-end models, that's exactly what they do! IEM's consists of a stereo pair of enclosures (including the drivers) which extend just past the second bend of your ear canals, and a cable with a connecor which you can plug into your home stereo, discman, etc... The manufacturer now sends your IEM's back to your audiologist.

FITTING
Your audiologist will test-fit your IEM's into our ears to make sure they'll peform properly, will show you how to care for & clean them, and will stress the importance of aural hygiene.

USES
In my work, these babies are used by musicians, but you can also get models which are designed for audiophiles. Optionally, you can combine these with a TST, and you've got the ultimate listening system, better that anything you're ever heard and almost entire in-audible to a person a foot away!

BENIFITS
(I'll just talk about the benifits for audiophiles here: If you'd like to know the additional advantages for concert musicians, drop me an email.)

As I just mentioned in the preceding paragraph, IEM's & TST's don't add noise to everyone else's life, so you can listen to your favourite music with pristine quality, or get wicked home theatre sound while someone is on the phone in the same room.

Secondly, since IEM's are custom-fitted to your ear canal, they also act as ear plugs, so they don't have to hit your ear drums as hard as a speaker since they don't have to compete with environmental sounds. This makes them much safer for your ears, since you get the sensation of high volume at substantially lower volumes than with speakers. If you were used to listening to your discman on the subway through headphones at "9", you'd only have to turn it up to "6" with IEM's and you'd still experience the same apparent volume without damaging your hearing!
Well, there you go: A brief introduction to In-Ear Monitors!