- slide 1 of 3
Optical & Electronic Viewfinders
While the mechanism for optical viewfinders is complex, essentially they consist of a series of mirrors that bounce incoming light in the lens barrel into the viewfinder and then into your eye—at least, SLR style viewfinders. Optical viewfinders may also consist of a mirror hole in the camera through which the composition is approximated, though there is that hefty problem of parallax. In either case, an inherent problem in optical viewfinders is that one cannot have a preview that accounts for such settings as exposure or color filters in digital cameras.
Electronic viewfinders have risen to largely replace optical viewfinders. Instead of seeing through the lens barrel, you see what the image sensor picks up on a miniature screen through the same viewfinder hole. While issues of whether the optical viewfinder is actually a fair representation of the photo or not have technically disappeared, many of these electronic viewfinders are of poor quality, being a relatively new concept with little development.
- slide 2 of 3
The Rise of LCD Screens
In many respects, LCD screens are what make digital cameras possible. After all, you need something like a computer screen to read the complexity of a computer output, which is what the plethora of menus and options on digital cameras have become.
Beyond pure necessity, they're also more convenient for many people. Instead of squinting one eye into a small hole that doesn't show you quite the image you'll be getting, you see things on a big bright LCD screen that you can even use to show other people miniatures of your photographic creations. Furthermore, LCD previews increasingly provide a more exact version of your image compared to viewfinders, especially with regards to techniques like manual focus for macro photography.
So, it should be somewhat unsurprising that many photographers, particularly casual ones, refrain from using viewfinders in favor of the LCD screen. Camera companies have picked up on this, and now many cameras don't even have viewfinders, and those that do tend be of relatively poor quality with little effort put into their development. Many professional photographers have begun to complain about the decreasing quality of viewfinders in DSLRs, pointing particularly to the decrease of coverage that the viewfinder provides relative to the picture you'll actually be taking, and the amount of magnification in the viewfinder itself. Little development has been put into creating usable electronic viewfinders that average consumers might at least be tempted to try, and quality optical viewfinders are an increasingly expensive rarity.
- slide 3 of 3
Viewfinders, both optical and electronic, still hold certain advantages over LCDs. For instance, LCD screen often catch the glare of the sun, making them impossible to read, making a viewfinder the only options. Viewfinders are also a far more stable option, as then the camera is stabilized against your face and is not held at arm's length. Some people cite reasons of tradition for continuing use; others, reasons of powersaving. Many photographers still swear by viewfinders.
Nonetheless, the fate of viewfinders remains to be seen, at least on a mass consumerism level.
For an example article on the mechanics of viewfinders and how their design has been decreasing in quality over the years, check out this article by Mike Johnston.
For a compare/contrast of LCD and viewfinder benefits, check out this article by Darren Rowse.