Since DisGirl did a "nook" explanation, I thought I'd throw in a Kindle one.
As with the plain nook, the plain kindles also use e-ink which means there is no glare outside (I LOVE THIS!). But there is also no lighting so you still need a booklight in the dark.
I think my Kindle will hold 3,000ish books they say.
There are 2 models of Kindles, 3G and Wifi. The Wifi ones require you to be somewhere there is a wifi connection. The 3G works off of cellular towers so if you can get Internet on a cellphone, you can download books off of the 3G. I also live in the woods and we have crappy Internet so I didn't want to have to rely on my Internet connection to download books so I opted for the 3G. I was even able to download a new release when I vacationed in Panama this summer with it. The 3G model's cost a little more, but there is no monthly charge for the 3G coverage. I'm buying my 11 year old daughter oen of the new Kindles that were just released this week (the Kindle Touch) for Christmas, and I'm opting to go with the 3G model for her as well. I just think in the long run it is worth those extra dollars.
The Kindles also have 2 options now where one has advertising and one does not. The ones with ads are cheaper than the ones without. Mine does not have ads, but it wasn't an option when I bought mine. If I was buying now, I'd buy with ads (my daughter's will be) . The ads do not appear on the screen when you are reading the book, but are on the screensavers. So they do not interfere with your reading at all! And some of the ads are really good deals (from what I've read) like a $100
amazon gift card for $50! I would have LOVED to have had that offer!
As a general rule, both the nook and Kindle require you to buy the books from their retailer (i.e. Barnes and Noble for Nook, Amazon for Kindle) but both have library checkout options if you have a library near you that participates. Mine doesn't so I do not have much experience with that. The digital forms of the books tend to be somewhat cheaper than the "real" books which I like.
Both of the devices offer LOTS of free books. I actually have bought very few books for my Kindle and I have a ton.
I'm not sure about the nook, but the kindle has a browser that you can surf the Internet with. It is limited and not so pretty, but it works (at least the 3G version has one, I'm not sure about the wifi). I took the battery out of my phone last summer when in Panama to be sure that I did not have any overseas charges, but used my Kindle to check email, facebook, and twitter daily. So it is functional.
You can probably tell that I LOVE my Kindle. I was actually very excited when my daughter asked for one for Christmas (so it's already preordered).
If you have any other questions, there are TONS of Kindle and Nook users here on the boards.