You can do so much more on a Kindle besides reading books. Here's a list of features I use. It is not comprehensive by any means.
Read books
I thought I should state the obvious, for the sake of completeness. Having a Kindle makes reading easy, because you can carry books around without incurring the cost of lots of weight.
I'm convinced that this, plus the option of obtaining free and low-cost books, can be used as selling points in trying to encourage people to read.
(For a list of 7 places you can get free or low-cost ebooks, read the article and the comment at 5 free and low-cost ebook websites.)
Read samples
If you're not sure if you want to buy a book, you can (usually) have a sample sent to your Kindle. This is a bit like the "Look inside" feature, but on your device rather than a screen.
Read periodicals
I read the New York Review of Books on my Kindle. It costs £2.99 a month, if my memory serves me well, and when it arrives every other Sunday it's really nice to read an article or two before even getting out of bed. So it's cheaper than the print edition, and more convenient to obtain.
Read PDFs
Rather than cart around printed PDFs, email them to your Kindle. You can find your Kindle's email address (and change it if you like), by logging in to your Amazon account, then clicking on Your Account, then Manage your content and devices. The second tab is a page listing your devices and their email addresses.
In the subject line of your email, write the single word Convert, and your Kindle will do the rest.
(Note that not all PDFs convert well. For an explanation, see 4 reasons your PDF report can't be read on a small device.)
Make notes
This is a feature that I find really handy. If you come across a passage that you'd like to cite in an article or an essay, you can select it and add a note to it.
Highlighting
Similar to making notes, but you just highlight the passage without adding anything yourself. You can also see what other people have highlighted.
I use the annotation and highlighting features to proofread my work while I'm on the move. It's not quite as useful as making marks on paper, but it's a pretty good second-best -- especially if the alternative is to not do it all. (I'm paranoid about annotating a load of sheets of my latest magnum opus, only to see them disappear in a gust of wind!)
Copy and paste your notes
Once you've annotated and highlighted bits of the book, go to your Amazon Kindle page. Did you know that such a thing exists?! Log in with your usual Amazon details, and then click on Your Highlights. You'll see this sort of thing:
See all your notes and highlights in one place.
You can then copy/paste the bit you want to cite, or look up the proginal passage right away. The only frustrating thing about all this is that although you can annote and highlight passages in a converted PDF document, those notes and highlights don't show up here.
As I said at the start of this article, I haven't listed all the features of the Kindle, just the ones I use a lot because I find them so useful.