Well, a rangefinder is a device used for measuring distance (bear with me - I am not being a smart ass). The classic rangefinders (before radio waves and laser beams vs time methods were introduced) used the very basis of trigonometry - if you know the distance between two points, and the angles at which lines leaving those two points must take to intersect with a third point - you can easily calculate how far that thisrd point is. You may have seen documentaries where soldiers would look through funny looking binoculars with the front elements spread really far apart - those are rangefinders.
Now, you can apply the same principle to focusing a camera - you just need two points some distance apart that will capture an image, and a lens that will move in a predetermined relationship with them. A rangefinder contains a viewing window and another one that projects an image into your viewfinder. You see the image through the viewfinder, and a ghost image projected via mirrors (usually)by the other viewing port. By moving the focusing ring on the lens, you rotate the second element until the image it projects is lined up with the actual image you see. Because of the predetermined relationship between the two ports and the lens - at that point you are focused.
In practice you see what you normally see in a camera viewfinder, plus a ghost image - movin the focus moves the ghost image. Line 'em up and you're done. Its really, really simple and very quick! Most RF cameras require less than 2/3 of a rotation of the focus ring to cover their entire range, and you can tell how far off you are by how far apart you are with your ghost image.
There are many medium format cameras in the RF configuration, by the way, not just 35mm.

Now, you may ask - if its so wonderful, why aren't all cameras RF's? Well, I don't know, they should be Just kidding!!!
The adventages of the RF are as follows:
-very quick focusing
-no need for a space and weight consuming, not to mention noisy, mirror. This also allows you to generally shoot at slower shutter speeds because the vibrations resulting from the mirror moving up and down are eliminated.
-as a result of the above, small size and light weight and whisper quiet operation (street photgrapher love them for hteir stealthy ways!)
-there is no "black out" when the mirror is up, as in an SLR, so you can see everything, all the time.

The disadventages:
- you are not looking through the taking lens - so there is something called paralax to adjust for (the fact that you looking through a point removed by a few cenitmeters from the actual lens) as you can imagine, the closer you get, the more off you will be. Most good rf's correct for that by moving the viewfinder as you focus, but a) it only goes so far (its like crossing your eyes after a certain point) and b) it makes the camera not very useful for extreme close up work, also, when you change lenses, you have to use reference lines or separate viewers to adjust for their field of view, where in an SLR - you see what the lens sees - wide angle? you see all that wide angle. telephoto? you see that magnified image exactly the way the film will.
-many rangefinders use leaf shutters - while they have their adventages, they are generally not capable of the very high speeds of most focal place shutters in SLR's.

Between those two points, the SLR wins the popularity contest due to its versitility and ease of use (and ease of getting used to various applications).

OK - I hope that about covers, sorry about the long winded response!


PS. You will most likely buy one sooner or later. They are cute, handy, charming, have personalities - you fall in love with them... its a sickness!!!

PPS. Here is a page that you may want to look at - this is a little known camera, but it is a classic rnagefinder layout, and there are many pictures which will hopefully help you make sense of my rambling (look at the picture of the camera with the top plate off to see more less how it works)