The screen on the Kindle 2 is your typical e-ink screen. It looks like newsprint or the slightly grey-green tinted paper that is found in some paperbacks. It has a matte finish that is in no way reflective except when a very bright light source is shining directly into the screen, at which point you will notice no real bright reflection pointing back at you, but rather a slight dispersed bit of light as you're most likely used to seeing reflected on some less glossy magazines. Holding the Kindle at a slight angle does away with this slight reflection and makes the text on the Kindle extremely crisp and clear for reading. If you've never used an e-ink display before, you'll be surprised by how much it behaves like actual paper. It loves light, and is perfect for taking a whole library of reading to very sunny places like the beach. There is no backlighting, or in fact any sort of lighting, with the e-ink screen. It is designed to function as paper and it does, with the notable exception of a quick flash of "ink" across the screen as you turn the page.
The screen in the 2nd generation Kindle measures 3.5 inches x 4.75 inches, displays sixteen shades of grey at a resolution of 600 x 800 pixels, and manages to turn the pages faster than the previous generation e-ink screens. On my first generation Sony Portable Reader, I had become accustomed to reading the last line or two of a page while clicking the next page button, so that I would finish just in time for the screen to refresh. On the Kindle 2, I'm much more naturally clicking to turn the page on the last few words. It's also a brighter overall "piece of e-paper" than the first generation screen that I had been used to using on my first generation Sony Portable Reader. There have been some complaints as of late about the new font-smoothing on the new Kindle making some smaller fonts appear too washed out and light, but as it only occurs with small fonts and the Kindle has the ability to toggle to larger-sized fonts it's something that I have not yet noticed in my testing except when browsing some websites with small fonts in the experimental web browser. This is not a problem with the Kindle's screen, however, but rather a software problem, and is something that Amazon should be able to fix with a firmware update, should the complaints continue.
Also, unlike the screens on your computer and cellphone, the Kindle's e-paper screen, like actual paper, can be touched by clean hands without leaving smudges and marks. The feeling of the screen is a bit smoother than the feeling of the white face of the device, but you can hold the device with your fingers touching the screen or read along with your finger underlining the text as you go, if that is your habit, without leaving big smudges that you must then read through or obsessively wipe away.