This mostly helps professional image editors, but regular folks can see a dramatic difference for certain types of images. In a sky like the blown-up image below, for instance, where there's a subtle gradation between shades of blue, you get nasty, stair-stepped "banding" with 24-bits (also called "8-bit color"). With 30-bits of color (normally referred to as "10-bit color") those gradations are smoothed out, resulting in a more natural image. For now, RAW photos will look better when displayed the new iMacs, but in the future, it may make help movies, too. Amazon, for one, supports extra colors with its 4K HDR streaming.
As we pointed out in our review, the latest iMac (2015) displays a wider range of colors thanks to its much-improved color gamut. It now outputs a higher color depth, too, which equates to more colors in total. Prior to the release of El Capitan, OS X was hampered by its 16 million color limitation -- Windows has supported 10-bit and higher ("deep color") output since version 7. That was never a big deal before, but Apple's latest 27-inch 5K iMacs apparently support the feature. If you're equipped with the latest Mac and have El Capitan, you can load up RAW photos with more than 8-bit color (not JPEGs) and you should see a difference. Apple still lists its 5K iMac screens having "millions" of colors, however, so we've reached out to see if the panels themselves support the feature.
Update: We've updated the post to clarify the difference between color range (gamut) and depth. Also, it's not entirely clear if any of Apple's 5K iMacs actually have 10-bit panels, so the post has been updated to reflect that. (Thanks, @ascaniocolonna.)
[Image credit: Wikimedia/Steve F]