Yes, there are actually numerous benefits you are missing, and none of them have anything to do with my "e-peen" as some other anonymous coward commented. The market for 30-and-higher bit display technologies is far from being electronic snake oil, I assure you; every movie you've ever seen in a digital cinema is projected at no less than 12 bits per colour component, for example -- considerably more colour than is supposedly "indistinguishable by the human eye" than my display is capable of reproducing.
I apologize if this comes across sounding tired and annoyed -- it is a little of both, admittedly -- but I tire of seeing this comment posted on discussion forums whenever "deep colour" displays are mentioned and hope you are genuinely interested as opposed to trolling.
It's trivially easy to illustrate how 24 bit displays are not beyond a human's ability to distinguish. Here's a simple test for you: Draw or display a gradient image from black to middle grey across the entire screen with no dithering. Can you see that there are bands of grey between those two values? You should have no difficulty whatsoever doing so (unless you have terrible vision). The fact that you can see those bands means you can easily distinguish between 16 million colours -- at least the way that colours are necessarily reproduced via red, green and blue channels.
Another easy experiment is to look at the colour "white" on your screen. Now look at a white sheet of paper held directly under a lamp, or out in direct sunlight. Sunlight is typically an order of magnitude brighter than most artificial light. If you can distinguish between 256 values between the blackest black and whitest white on your monitor, and the white outside is an order of magnitude brighter than the brightest white on your monitor, then you have just illustrated that you are theoretically capable of discerning more than 2500 shades of "grey" without even introducing any individual colours yet.
That said, the prime benefit of deep color monitors isn't that they can display all those colours simultaneously -- most software can't do that yet (despite microsoft's promise that Windows 7 would; even Adobe has as much as said that doing so would involve some serious rewrites to be able to display more than 8 bits per channel even though it can manipulate images with higher bit depths in memory).
The two primary benefits of deep colour monitors are A) A wider colour gamut than most monitors, particularly that of other LCDs; the colours are richer and more vibrant, and can completely encircle a colour space such as sRGB instead of covering most of it (which is the best most LCDs can do); and, more importantly, B) the monitor is internally capable of representing all of those colours, which is particularly important when displays are colour-calibrated.
The latter point is particularly important to prevent actual loss of colour. Remember the banding part I mentioned earlier? Well, banding becomes more prominent when displays are colour-corrected because an 8-bit monitor can only reproduce 16 million colours. When the display is calibrated, a lookup table or matrix is used to "transform" an absolute colour value -- say, a perfectly neutral 50% grey -- into what actually appears as being a perfectly neutral 50% grey on your display, which may in fact be something like (132,129,124) on your display if it has a blue cast like most LCD-backlit displays do. Because of this correction, you "lose" a lot of colours on your display because they fall outside the calibrated table, meaning your 16 million colours might be more like 12- or 13-million by the time you're done. This is unfortunately less trivially easy to experience -- especially if you don't have access to a colorimeter to calibrate your display or weren't at least provided with (and use) an ICM/ICC file by your display manufacturer -- but it is a well-documented phenomenon you'll see illustrated on LCD test suites like Lacom's (http://www.lagom.nl/lcd-test/gradient.php).
Last but not least, part of the reason for purchasing the display wasn't just its abilities, but because good colour-critical displays also have very good brightness levels, viewing angles, completely consistent colour consistently across the entire surface of the display, and no infuriating backlight bleeds at the top/bottom of the screen even in complete darkness. The monitor also has a three-year, on-site warranty, which was a big draw for me after having two monitors in a dual-monitor rig fail on me within a week of one another and having multiple terrible service experiences in the RMA process.
As for the other comment about how nobody would get anything extra out of it, that's not true at all; most people still buy a whole computer from a vendor which typically come with a color profile for the display device pre-installed. Yes, it's "factory calibrated" (which means each devices gets a generic profile that somewhat resembles the device) but it's better than nothing, and the end-user doesn't have to do, install or own anything special to take advantage of it.
Further, I will point out that I do indeed do web design (as I mentioned) but also significant amounts of photographic work as part of my business, where colour is important not only for the web (because many browsers can now parse embedded colour profiles, as I already stated) but also for accurate colour work intended for other output mediums as well, such as print and projection.
Last but not least, the comment stating that, "a lot of people won't have calibrated displays so the effort is worthless," is as ridiculous as dismissing any other standard because it would place a burden upon you to be bothered to follow it.
Just as with any other standard, the purpose of accurate colour representation for designers isn't the expectation that it's going to display exactly the same on your screen as it does mine -- or even that the same image on the same screen is going to look the same to my eyes as it does your eyes -- but that it is supported by a widely supported standard, quantitative measurement that CAN be followed, as opposed to your apparent, "Well it looks fine to me so fuck you, your shit must suck," attitude that would somehow be a more appropriate professional response to a customer complaining that a colour seems off to them on their so-so laptop display.